A generalized formula is derived for the electron emission current in relation to the temperature, the electric field, and the electronic work function for a “metal–dielectric” system. The formula takes into account the quantum nature of the image forces. In deriving it, the Fermi–Dirac distribution and the quantum image potential obtained in terms of the electron–polaron theory are used. In the limit of the classical potential of image forces, the well-known Richardson–Schottky and Fowler–Nordheim formulas are obtained for thermionic emission and field emission, respectively. It is shown that at high temperatures and electric fields E ≥ 10 MV/cm, the polaron contribution to the electron emission current increases with increasing field and decreases with increasing temperature. The decrease in current is related to an increase in effective electronic work function due to the electron-polaron effect. Extrapolation formulas convenient to obtain theoretical estimates are derived for the thermionic and the field emission current.