The non-Markovian encounter theory is reformulated and used to find the quantum yields and kinetics of reversible energy transfer. Assuming a short range interaction between the particles, the kinematic approximation is employed to determine the integral kinetic equations and following from them differential equations of encounter theory. The differential variant of the theory is shown to be less appropriate since it fails to describe delayed luminescence during encounter : The reaction constant diverges with time when the acceptor of energy decays slower than the energy donor. On the contrary, integral encounter theory is very suitable for calculating the quantum yields and dissipation kinetics at any ratio between decay times.