The cosmic-ray (CR) electrons and positrons in space are of considerable significance for studying the origin and propagation of CRs. The satellite-borne detector Dark Matter Particle Explorer (DAMPE) has been used to measure the separate electron and positron spectra, as well as the positron fraction. In this study, the Earth's magnetic field is used to distinguish CR electrons and positrons, as the DAMPE detector does not carry an onboard magnet. The energy for the measurements ranges from 10 to 20 GeV, which is currently limited at high energy by the zenith-pointing orientation of DAMPE. The results are consistent with previous measurements based on the magnetic spectrometer by AMS-02 and PAMELA, whereas the results of Fermi-LAT appear to be systematically shifted to larger values.