PHYSICS
posted by Bubbles .
Consider a one layer atmosphere for the planet Venus. 19% of incoming solar radiation is absorbed by the atmosphere. 99% of the outgoing radiation is absorbed by the atmosphere. The incoming radiation, E, as measured by satellite is 615 Wm2.
1) Derive two equations, one for the top of the atmosphere and the other for the Venusian surface in terms of x, y and E. Solve for the surface and atmospheric temperatures.

That value of E is wrong. It is lower than the value at the earth's orbit. It should be higher.
See
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Assuming your value of E (unlikely):
At equilibrium, the same amount is radiated back as hits the ground or the ground would keep heating forever.
(1.19) * 615 w/m^2 hits ground
Therefore at what Kelvin temperature is the radiation 498 w/m^2 ? That is the ground temperature.
The atmosphere is abosrbing .19(615) = 117 w/m^2 inbound + .99 (498)= 493 outbound so it radiates back a total of 610 w/m^2. Again find the temp in deg. Kelvin.