The detection of primary cosmic ray electrons with energies above 1 TeV implies the existence of a nearby, r\ensuremath{\le}100 pc, and relatively young, t\ensuremath{\le}${10}^{5}$ yr, source(s) of accelerated electrons. Therefore a correct treatment of the formation of the spectra of electrons during their propagation in the interstellar medium requires a separate consideration of the contribution of one (or a few) nearby source(s) from the contribution of distant (R\ensuremath{\ge}1 kpc) sources. To implement this approach, the problem of energy-dependent diffusive propagation of relativistic particles from a single source is considered, and the analytical solution to the diffusion equation in the general case of arbitrary energy losses and injection spectrum of primary particles is found. We show that in the framework of the proposed two-component approach, i.e., separating the contribution of the local (discrete) source(s) from the contribution of distant sources, it is possible to explain all the locally observed features of the energy spectrum of cosmic ray electrons from sub-GeV to TeV energies. In addition, assuming that the local source produces electrons and positrons in equal amounts, the model allows us to explain also the reported increase of the positron content in the flux above 10 GeV.