We have implemented a Monte Carlo simulation method to study electron emission from solid surfaces under electron irradiation at energies of up to 100 keV. Calculations are performed for the yields and energy distributions of the emitted electrons in backscattering and transmission geometries for Al and Au metals. For transmission studies the film thicknesses range from a few nanometres to micrometres. The method is demonstrated to predict correctly the electron backscattering and transmission properties, and gives a qualitatively reasonable description of the low-energy (E < 50 eV) secondary electron emission. For the exit surface of thin films we predict a universal behaviour according to which the maximum low-energy secondary electron yield is obtained when similar to 50-70% of the incident electrons are transmitted through the film. This corresponds to film thicknesses of similar to 0.75 times the mean depth of penetration of the electron with the same kinetic energy in a bulk target