A differential-integral equation system of Holstein type is used to describe the kinetic process in V-E energy transfer between molecules and atoms with radiation trapping.A reduced solution of a finite series has been presented,which allows to describe the whole temporal behavior of fluorescence.The further derivative is an analytical expression of the fluorescence decay rate as a function of rate constants and the maximum eigenvalue of the integral operator appearing in the rate equations.This will be especially useful and convenient for experimental determinations.Results are schematically illustrated and mutually compared by means of numerical calculations.