The proton electromagnetic form factors are essential pieces of our knowledge of nucleon structure. However, Rosenbluth separation measurements of the proton electric form factor, $G_E(Q^2)$, differ from polarization transfer measurements by a factor of three at $Q^2 = 5.6$ (GeV/$c$)$^2$. This discrepancy must be resolved. One possible resolution is to include the difficult-to-calculate contribution of hard two-photon exchange (TPE) contributions. This contribution is directly proportional to the difference between positron-proton and electron-proton elastic scattering cross sections. We directly determined the TPE effect by measuring the ratio of the positron-proton to electron-proton elastic scattering cross sections, $R=\sigma(e^+p)/\sigma(e^-p)$ over a wide range of momentum transfer, $Q^2$, and virtual photon polarization, epsilon, using a mixed beam of electrons and positrons in Hall B. This talk will describe the experimental techniques used to produce this beam, the analysis techniques to identify elastic scattering events, and some preliminary results.