A large evacuated chamber is maintained at a constant temperature $T_0$. Two black bodies $A$ and $B$ are situated in the enclosure, not touching, with body $A$ maintained at temperature $T_1\left(T_1>T_0\right)$. When $B$ is at $T_0$ the rate of loss of heat from $A$ is $W_1$ and when $B$ is at $T_1$ the rate of heat loss from $A$ is $W_2$. Show that $A$ experiences no net loss of heat by radiation when the temperature of $B$ is $T_2$, given by
$$
T_2^4=\frac{W_1 T_1^4-W_2 T_0^4}{W_1-W_2}
$$