The end-to-end diffusion dynamics of an ideal Rouse chain in solution, as estimated by fluorescence resonance energy transfer between the chain ends via Forster mechanism, is investigated theoretically through a non-Markovian reaction-diffusion equation. The resulting equation, with as well as without the memory term included, is solved numerically and the calculated survival probability, especially in the presence of memory term, compares extremely well with the recently reported Brownian dynamics simulation data for a variety of choice of Forster transfer parameters.