A measurement of the energy spectra of cosmic-ray positrons and electrons was made with a balloon-borne magnet-spectrometer, which was flown at a mean geomagnetic cut-off of 4.5 GV/c. The observed positron flux in the energy range 7-16 GeV is approximately an order of magnitude lower than that of electrons, as measured in other experiments at various energies. The power law spectral index of the observed differential energy spectrum of electrons is -2.89 +/- 0.10 in the energy interval 7.5-47 GeV. For positrons the overall fit of the available data above 7 GeV has been considered. The spectral index is found to be -3.37 +/- 0.26 and the fraction of positrons, e+/(e+,+ e-), has a mean value of 0.064 +/- 0.003. The world data on e+/(e+,+ e-) from 0.1 to 30 GeV indicate that a plerion type electron spectrum is preferred over the other types. The trend of the presently existing high energy data also suggests a possible contribution of positrons produced at the pulsar polar cap. High resolution experiments capable of identifying positrons at least up to 100 GeV with high statistics are required to pinpoint the origin of both electrons and positrons in the cosmic radiation.