We present a measurement of the combined $\nu_e$ + $\bar{\nu}_e$ flux-averaged charged-current inclusive cross section on argon using data from the MicroBooNE liquid argon time projection chamber (LArTPC) at Fermilab. Using the off-axis flux from the NuMI beam, MicroBooNE has reconstructed 214 candidate $\nu_e$ + $\bar{\nu}_e$ interactions with an estimated exposure of 2.4$\times10^{20}$ protons on target. Given the estimated purity of 38.6\%, this implies the observation of 80 $\nu_e$ + $\bar{\nu}_e$ events in argon, the largest such sample to date. The analysis includes the first demonstration of a fully automated application of a dE/dx-based particle discrimination technique of electron and photon induced showers in a LArTPC neutrino detector. We measure the $\nu_e + \bar{\nu}_e$ flux-averaged charged-current total cross section to be ${6.84\pm\!1.51~\textrm{(stat.)}\pm\!2.33~\textrm{(sys.)}\!\times\!10^{-39}~\textrm{cm}^{2}/~\textrm{nucleon}}$, for neutrino energies above 250 MeV and an average neutrino flux energy of 905 MeV when this threshold is applied. The measurement is sensitive to neutrino events where the final state electron momentum is above 48 MeV/c, includes the entire angular phase space of the electron, and is in agreement with the theoretical predictions from \texttt{GENIE} and \texttt{NuWro}. This measurement is also the first demonstration of electron neutrino reconstruction in a surface LArTPC in the presence of cosmic ray backgrounds, which will be a crucial task for surface experiments like those that comprise the Short-Baseline Neutrino (SBN) Program at Fermilab.