There is a significant discrepancy between the values of the proton electric form factor, $G_E^p$, extracted using unpolarized and polarized electron scattering. Calculations predict that small two-photon exchange (TPE) contributions can significantl
y affect the extraction of $G_E^p$ from the unpolarized electron-proton cross sections. We determined the TPE contribution by measuring the ratio of positron-proton to electron-proton elastic scattering cross sections using a simultaneous, tertiary electron-positron beam incident on a liquid hydrogen target and detecting the scattered particles in the Jefferson Lab CLAS detector. This novel technique allowed us to cover a wide range in virtual photon polarization ($varepsilon$) and momentum transfer ($Q^2$) simultaneously, as well as to cancel luminosity-related systematic errors. The cross section ratio increases with decreasing $varepsilon$ at $Q^2 = 1.45 text{ GeV}^2$. This measurement is consistent with the size of the form factor discrepancy at $Q^2approx 1.75$ GeV$^2$ and with hadronic calculations including nucleon and $Delta$ intermediate states, which have been shown to resolve the discrepancy up to $2-3$ GeV$^2$.
