Grazing-incidence Rutherford backscattering and angle-resolved x-ray photoelectron spectrometry are used to determine the ion-concentration profiles near the surface of a solution consisting of a salt (TEABr) in a weakly polar organic liquid (polyethylene glycol) with atomic-layer depth resolution. The predictions of a model, in which ions in solution are repelled from the surface due to a screened Coulomb interaction with their image charge, are in good agreement with measured ion profiles. This contrasts with the behavior of salts in aqueous and highly polar organic solutions.