We developed a theory of excitation energy transfer (EET) which is applicable to all the values of the coupling strength U in the presence of homogeneous and inhomogeneous broadening. In constructing the theory, we adopted a decoupling procedure corresponding to the factorization by a two-time correlation function of the excitation transfer interaction in the integro-differential equation of a renormalized propagator. We also assumed that the two-time correlation function decreases exponentially with time. Under these assumptions, we could handle our theory nonperturbatively and analytically. We derived formulas of criteria among exciton, intermediate coupling, and Forster mechanisms. We exploited a novel method for determining the EET rate applicable to all the mechanisms from Forster to exciton. Then, we obtained compact formulas for the EET rate and the degree of coherency involved in the EET. We demonstrated how the exciton state is destabilized by the presence of inhomogeneity in the excitation energy of the constituents. The theory was applied to a light-harvesting system LH2 of photosynthetic bacteria.