Researching resonance energy transfer (RET) from one quantum emitter to another in the strong coupling regime can provide a new route to empower ultrafast quantum manipulations and possess fascinating technological frontiers. However, most of the reports only discussed the weak electronic coupling limit and incoherent energy transfer. Here, we establish a universal theory to investigate RET between two emitters weakly/strongly coupled to a plasmonic mode and analyze the dynamics of RET by utilizing a full-quantum method. Combining with our theory, we investigate the RET rate of a multilayer system in which J-aggregates/monolayer WS2 acts as the donor/acceptor. The calculated results verify that RET rates in the strong coupling regime increase two orders of magnitude compared to the weak coupling regime. Moreover, the coherent energy exchange between two detuned emitters is realized in the strong coupling regime by the time-dependent population calculations. The double Rabi splitting appears in the photoluminescence (PL) spectrum with sufficient RET rates (103ns−1) and coupling strength (g=60 meV). Our work demonstrates a quantitative calculation of RET rates and PL spectrum for the plasmon-biexciton coupled systems, providing a promising way for precise photochemical control, integrated optical device design and quantum information processing.