Hi Hill, thank you for your reply.
I understand your point:
\delta T_A = \frac{\partial f}{\partial E}\bigg\rvert_{T_A} \delta E_A and
\delta T_B = \frac{\partial f}{\partial E}\bigg\rvert_{T_B} \delta E_B .
However, since the two subsystems are not necessarily equal, even though \delta...