A thermodynamic theory is developed for obtaining the enthalpic and entropic contributions to the surface excess Gibbs energy of electrolyte solutions from the dependence of the surface tension on concentration and temperature. For elaboration, accurate activity coefficients in solution as functions of concentration and temperature are required. The theory is elaborated for (1-1) electrolytes and applied to HClO(4), HNO(3), NaCl, NaBr, and LiCl, of which the first two adsorb positively and the other three negatively. One of the conspicuous outcomes is that in all cases, the surface excess entropies slightly decrease with electrolyte activity but remain close to that of pure water, whereas the enthalpy is different from that. The implication is that the driving force for positive or negative adsorption must have an enthalpic origin. This finding can be useful in developing and evaluating theoretical models for the interpretation of surface tensions of electrolyte solutions.