The original integral encounter theory (IET) was used to describe the kinetics and quantum yield of fluorescence in the presence of intense pumping light. We compare the energy quenching through an impurity induced interconversion, with energy quenching produced by bimolecular charge transfer from the excited donor to the acceptor of the electron. In the former case, the convolution recipe which expresses the quantum yield via the system response to delta-pulse excitation is confirmed under special conditions, while in the latter case it was shown to not be applicable at all. By means of IET we found the stationary concentrations of excitations and ions and demonstrated the qualitative violation of the classical Stern-Volmer law at high intensity of pumping light. The modified form of this law was proposed instead and the light dependence of its constant was determined in the contact approximation.