Unidirectional electronic excitation energy transfer from a photoexcited donor chromophore to a ground state acceptor chromophore - both linked by a rigid bridge - has been investigated by low temperature high-resolution single molecule spectroscopy. Our approach allows for accurately accessing static disorder in the donor and acceptor electronic transitions and to calculate the spectral overlap for each couple. By plotting the experimentally determined transfer rates against the spectral overlap, we can distinguish and quantify Förster- and non-Förster-type contributions to the energy transfer.