The future space-based GAMMA-400 scientific observatory is being developed under the Federal Space Program of Russian Federation in the period from 2016-2025. This observatory includes a γ-ray telescope, which will detect gamma rays in the energy range from ~20 MeV to several TeV with high angular and energy resolutions and cosmic-ray electrons + positrons up to several tens of TeV using main and lateral appertures. Recent experimental observations indicate a possible existence of a break in the electrons + positrons spectrum at around TeV energies. A number of speculations to explain this phenomenon have arisen. This article presents the method of high-energy electrons detection from the lateral aperture of the GAMMA-400 gamma-ray telescope. This method implements the machine learning analysis and provides the high-energy proton background rejection at the level of 10$^4$ in the energy range from 100 GeV to 10 TeV. The effective acceptance for electron detection with such proton rejection is about 0.52 m$^2$×sr for the four lateral sides of the GAMMA-400 gamma-ray telescope. This effective acceptance exceeds by several times that of CALET and DAMPE experiments. This capability of our instrument will allow to improve significantly the measurements of electron + positron flux above 1 TeV and, hence, understand better the debatable spectrum break.