  An exact solution to the interaction between two emitters mediated by
F\"{o}rster resonance energy transfer is presented. The system is comprised of
a one-dimensional optical waveguide with two embedded two-level systems and is
analyzed using a recently developed quantum-field theoretical approach. This
exactly solvable model features several competing mechanisms that lead to a
rich physical behavior such as, for instance, the possibility to change from an
attractive to a repulsive interaction. Our nonperturbative analysis allows on
very general grounds to describe the interaction as a truly non-Markovian
phenomenon mediated by the atom-photon bound states of the system. These
results are of direct relevance for energy or information transfer processes as
well as for atom trapping more complex systems.
