Radiation heat transfer between parallel plates

[hmmm27]

is there a way to calculate the final temperatures of the plates (in steady state, when the amount of heat known from above equation will be exchanged)?

$T_{final}$ given $T_1$ and $T_2$ ? Stefan-Boltzmann equation : juggling, thereof.

For the two values given : 293.15K , 373.15K , the results of that (radiative) and the heat-conduction equation mentioned differ by ~2%.

Do the algebra first. Waaaay less messy.