We investigate resonance energy transfer (RET) between a donor-acceptor pair above a gold surface (including bulk and thin-film systems) and explore the distance/frequency dependence of RET enhancements using the theory we developed previously. The mechanism of RET above a gold surface can be attributed to the effects of mirror dipoles, surface plasmon polaritons (SPPs), and retardation. To clarify these effects on RET, we analyze the enhancements of RET by the mirror method, the decomposition of s- and p-polarization, and the SPP dispersion of charge-symmetric and charge-antisymmetric modes. We find a characteristic distance (approximately 1/10 of the wavelength) that can be used to classify the dominant effect on RET. Moreover, the characteristic distance can be shortened by narrowing the thickness of the thin-film systems, indicating that SPPs can enhance the rate of RET at a short range. The charge-symmetric and charge-antisymmetric modes of the thin films also allow us to engineer the maximum RET enhancement. We hope that our analysis inspires further investigation into the mechanism of RET coupled with SPPs and its applications.