A Green's function approach to nonlinear electronic transport in a static electric field is developed microscopically for the system composed of interacting electrons with impurities and phonons. The essemtoal idea is to separate the center-of-mass motion of electrons. An electron temperature is introduced as a measurement of the internal energy of the relative electrons electrons and phonons in the initial state, we obtain the density matrix for the electron-lattice sysytem to the first order of mass of interaction but nuder arbitrarily strong electric field. The frictional force experienced by the center of mass of the Green's-function technique, and the force-and energy-balance equations for steady state are obtained. These equations are qpplied to the calculations of the ratio of electron temperature to the lattice temperature and the electron redsistivity as functions of drift velocity imputity, acoustic-phonon, and optcal-phonon scatterings. The dynamic nature of Coulomb screening by charge carriers is studied numerically. One of the interesting predictions is the possible cooling of electtons at low temperatures in samples with low impurity comcentration.