We present measurements of the E-mode polarization angular auto-power spectrum (EE) and temperature--E-mode cross-power spectrum (TE) of the cosmic microwave background (CMB) using 150 GHz data from three seasons of SPTpol observations. We report the power spectra over the spherical harmonic multipole range 50< {\ell }<=slant 8000 and detect nine acoustic peaks in the EE spectrum with high signal-to-noise ratio. These measurements are the most sensitive to date of the EE and