The solution of the Klein-Gordon and Dirac equation for the propagator (Green's function) in the very-high-energy limit (1/{ital E} approximation) is studied in the context of quantum beamstrahlung.'' The results obtained are necessary to consider bremsstrahlung energy loss by electrons and positrons in high-energy {ital e}{sup +}{ital e}{sup {minus}} linear colliders when multiphoton radiation processes are taken into account. The results can be useful also in other physical processes, e.g., photon radiation in crystals.