An exact integral equation is derived for the backscattering coefficient as a function of energy and angle. The equation has an approximate symmetry which allows one to determine the conditions under which backscattering will be independent of the energy of the incident electrons. The validity of some approximations is discussed, and a possible method for obtaining numerical solutions is proposed. It is found that small and large-angle individual scatterings are of about equal importance. For those electrons that have lost very little energy, the equation can be solved exactly, and some interesting results are obtained.