Förster resonance energy transfer (FRET) is an important method in studying biochemistry reactions. But quantifying FRET rapidly is difficult to do because of crosstalk between free donor, free acceptor and FRET fluorescent signals when only excitation or emission property of a FRET sample is measured. If FRET is studied with excitation-emission matrix (EEM) measurements, because the fluorescence intensity maxima of donor, acceptor, and FRET emissions occupy different regions within the EEM, FRET fluorescence can be easily separated out by linear unmixing. In this paper, we report a novel high-speed Fourier Fluorescence Excitation Emission spectrometer, which simultaneously measures three projections of EEM from a FRET sample, which are excitation, emission and excitation-emission cross-correlation spectra. We demonstrate that these three EEM projections can be measured and unmixed in approximately 1 ms to provide rapid quantitative FRET in the presence of free donors and acceptors. The system can be utilized to enable real-time biochemistry reaction studies.