Electron differential inverse mean free paths for volume-plasmon excitations and differential probabilities for surface-plasmon excitations have been calculated using dielectric response theory. A model dielectric function which satisfied sum rules and agreed with optical data was established for these calculations. In surface-plasmon calculations, we considered electron-impact emissions of the reflected electron-energy-loss spectroscopy. Formulations were made for obliquely incident electrons with the recoil effect and without the small-scattering-angle assumption. For volume-plasmon excitations, we evaluated corrections due to the exchange and Z13 effects. Comparison between calculated results and experimental data extracted from reflected electron-energy-loss spectra showed good agreement. Calculated differential cross sections have been used to solve the transport equation for the angular and energy flux spectra of reflected electrons. Contributions to the spectra from single and plural plasmon excitations were analyzed. It was found that calculated spectra were in good agreement with measured data.