Ok, I know this isn't computer related but there seems to be a bunch of knowledge in here so maybe someone can help.
My goal is to have an electric fence around some corn and other stuff I am growing to keep out the critters. The hot fence is already up and I have an electric fence emitter but running an extension cord out to it is getting old. I want to do it solar and would like to do it with the stuff I already have if possible. So here is what I have...
 
The fence emitter (input on it is 110-120 VAC, .10 amps, 60 hz, 10 watts)
A 12 volt car battery
A small 12 volt solar panel rated at 350mA, 5 watts
A car style inverter ,12v cigarette style plug to a standard 120 plug, 150 watts
 
I can't do math and I am thinking I can't just wire all this up. It seems like I need something else to keep the inverter from getting the power from the solar panel. Looking at the math, If I did figure out how to hook this up, will my battery run dead since the panel is half the wattage? The emitter is a pulsing type, not a constant shock but I don't know if that matters. I know the solar emitters are not that much but I want to use this solar panel for something. The almighty go to google is just trying to sell me solar units or finding coils to use with batteries to make fences. Any ideas?

I think you are right. Probably just easier to bury some romex wire and make a plug out there. Just wanted to use the battery and solar panel.

We have switched more than half of our house to LED lights. Now that it's summer, there is a huge difference in my music room with the led bulbs. The room is fairly small and with all the sound proofing, it gets hot in there and the old style lights made it like an oven. Maybe I will use the panel for an exhaust fan in the garage or something.

agent8
Ok, I know this isn't computer related but there seems to be a bunch of knowledge in here so maybe someone can help.
My goal is to have an electric fence around some corn and other stuff I am growing to keep out the critters. The hot fence is already up and I have an electric fence emitter but running an extension cord out to it is getting old. I want to do it solar and would like to do it with the stuff I already have if possible. So here is what I have...
 
The fence emitter (input on it is 110-120 VAC, .10 amps, 60 hz, 10 watts)
A 12 volt car battery
A small 12 volt solar panel rated at 350mA, 5 watts
A car style inverter ,12v cigarette style plug to a standard 120 plug, 150 watts
 
I can't do math and I am thinking I can't just wire all this up. It seems like I need something else to keep the inverter from getting the power from the solar panel. Looking at the math, If I did figure out how to hook this up, will my battery run dead since the panel is half the wattage? The emitter is a pulsing type, not a constant shock but I don't know if that matters. I know the solar emitters are not that much but I want to use this solar panel for something. The almighty go to google is just trying to sell me solar units or finding coils to use with batteries to make fences. Any ideas?

My guess is the fence emitter uses little to no power unless its actively shocking something. If you have something to measure the power draw of the fence emitter while it's hooked up to a normal outlet you should see how much power it actually draws while its "idle". If its a trivial amount its possible that using the solar panel to keep the battery charged is a viable solution, especially during the summer when you have ~15+ hours of daylight. 
 
I might start by seeing if you can even charge the battery with the solar panel. Even if it can actually hit its rated 12v\350ma, that might not be enough to charge the battery. I would drain the battery and hook up the solar panel to it in the morning and measure the voltage of the battery every couple of hours and see if it's going up at all. I'd check to see if it's safe to just hook the solar panel up straight to the battery first though. I'm pretty sure you can hook up a normal car battery straight to a DC power source to charge it, but I'm not 100% certain of this. 
 
You also might want to try to test the lower voltage limit of the inverter, because in all likely hood you'll be running it well below its rated voltage. I think most are designed for a ~14v power source, and your battery will likely be well below 12v. Its possible it has a low input\output voltage protection and simply won't work at such a low input voltage. 

I have been working on my own solar projects for years.  Let me start you off with this advice, prepare for wattage losses everywhere in the system.  Nothing is 100% efficient, there is always a loss somewhere.
 
So to start the math, first you would need to know your solar hours in your area.  Even if there is 12 hours of daylight, the solar panel is only really able to use 6 of the 12 hours.  Second would be the solar panel, it too only gets a percentage of light unless angled directly facing the sun all the time.  Example, my 50W PV is able to produce 35W when facing South at a fixed angle, 50W if tilted at the sun. 
 
Inverters are another loss of power, usually around 80% or less efficient.  There are two types of inverters, pure-sine wave (also known as true-sine wave) and square-sine wave.  Pure-sine wave inverters are the best choice as many electronic devices will accept them as these types of inverters produce a sine wave close to that what comes out of the house hold outlet.  Square-sine wave inverters mimic the power sine wave that comes out of a house hold outlet, but does so in steps to produce the AC wave form.  Thus these inverters are best for dumb devices like light bulbs.
 
Charge controllers can play a major role of getting the maximum wattage from the PV panels.  There are three types, on/off relay, PWM and MPPT.  The on/off relay type are the simplest and most damaging for batteries as they connect and disconnect at a set voltage point.  Too much applied voltage can cook a battery bank.  PWM are the second best and preferred for small projects.  They will regulate PV voltage incoming into the battery bank and maintain a constant charge as long as the PV voltage is higher than the battery bank.  MPPT is the best charge controller, but also the most expensive.  These charge controllers use DC-DC voltage conversion to get the most wattage out of the PV panel.  Even if the PV system is producing 10V @ 20W, the MPPT will be able to convert the voltage up higher to match the battery bank voltage while maintaining close to the 20W or less.
 
As for your solar electric fence, the inverter will be the issue.  With that small of a PV panel and the fact the inverter will constantly use power when plugged in, your battery will mostly run empty in a few days if not hours (depending of the size of the battery).