You have two equilibrium equations, one for the atmosphere and one for the surface of the Earth, and two unknowns, Ta and Te, so you should be able to solve them. You can set up the equations by looking at where the arrows originate or end. For the surface of the Earth there are two arrows coming in and one going out, and they've pretty much told you what those terms are, so just write the equilibrium equation where what goes out must equal what comes in. Same thing for the atmosphere, except there you have one coming in and three going out.
The energy absorbed by greenhouse gases causes the equilibrium surface temperature to be higher.
There is NO **man-made** Global Warming and there has never been any.
What global warming? It's been cooling for at least 12 years according to HadCrut3 & HadCrut4 is nearly flat. http://www.woodfortrees.org/plot/hadcrut...
According to RSS Satellite data there has been no warming for more than 18 years.
Here are some lectures: http://forecast.uchicago.edu/lectures.ht...
And here are a few online models: http://forecast.uchicago.edu/models.html
Much of the lectures deal with the image posted.
