The electron (anti-)neutrino component of the T2K neutrino beam constitutes the largest background in the measurement of electron (anti-)neutrino appearance at the far detector. The electron neutrino scattering is measured directly with the T2K off-axis near detector, ND280. The selection of the electron (anti-)neutrino events in the plastic scintillator target from both neutrino and anti-neutrino mode beams is discussed in this paper. The flux integrated single differential charged-current inclusive electron (anti-)neutrino cross-sections, $d\sigma/dp$, and the total cross-sections in a limited phase-space in momentum and scattering angle ($p > 300$ MeV/c and $\theta \leq 45^{\circ}$) are measured using a binned maximum likelihood fit and compared to the neutrino Monte Carlo generator predictions, resulting in good agreement.