A solid sphere and a hollow sphere made of the same material and...

The rate of emission of radiation by a body is given by Stefan-Boltzmann law:

$E = e \sigma A T^4$

Since both the solid and hollow spheres have the same radius, their surface areas $A$ are equal. Being made of the same material, their emissivities $e$ are equal. As their initial temperatures $T$ are identical, both spheres will emit an equal amount of radiation per unit time in the beginning.

The rate of absorption of radiation from the surroundings is given by:

$P_{abs} = a \sigma A T_0^4$

where $T_0$ is the temperature of the surroundings and $a$ is the absorptivity. Since $a$ and $A$ are the same for both spheres, they will absorb an equal amount of radiation from the surroundings.

The rate of cooling is given by:

$\dfrac{dT}{dt} = \dfrac{e \sigma A (T^4 - T_0^4)}{mc}$

Since the solid sphere has a greater mass $m$ than the hollow sphere, its initial rate of cooling will be lesser. Consequently, their temperatures will differ at any subsequent instant.