There are two kinds of well-known electron emissions from metal: field and thermionic emission. For thermionic emission, electrons come out of a metal due to the thermal energy, whereas for field emission, electrons tunnel out of a metal through the strong electric field. In this study, the most general electron emission caused by the temperature and electric field with a free electron gas model was considered. The total current density of electron emission comes from the field emission effect, where the electron energy is lower than vacuum, and from the thermionic-emission effect, where the electron energy is higher than vacuum. The total current density of electron emission is shown as a function of the temperature for a constant electric field, and as a function of the electric field for a constant temperature.