The total cosmic ray electron spectrum (electrons plus positrons) exhibits a break at a particle energy of $\sim 1\rm~TeV$ and extends without any attenuation up to $\rm \sim 20~ TeV $. Synchrotron and inverse Compton energy losses strongly constrain both the age and the distance of the potential sources of TeV and multi-TeV electrons to $\rm\approx 10^5~yr$ and $\rm \approx 100-500~pc$, depending on both the absolute value and energy dependence of the cosmic ray diffusion coefficient. This suggests that only a few, or just one nearby discrete source may explain the observed spectrum of high energy electrons. On the other hand the measured positron fraction, after initially increasing with particle energy, saturates at a level well below 0.5 and likely drops above $\sim 400-500$ GeV. This means that the local source(s) of TeV electrons should not produce positrons in equal amount, ruling out scenarios involving pulsars/pulsar winds as the main sources of high energy leptons. In this paper we show that a single, local, and fading source can naturally account for the entire spectrum of cosmic ray electrons in the TeV domain. Even though the nature of such source remains unclear, we discuss known cosmic ray accelerators, such as supernova remnant and stellar wind shocks, which are believed to accelerate preferentially electrons rather than positrons.