In general, adsorption enthalpies of surfactants adsorbing on solid particles from aqueous solutions are determined either by calorimetry or by the indirect (isosteric) method, based on the Clausius-Clapeyron equation. This paper is the first part, of a two-part contribution dealing with a comparison of both methods. In the present part adsorption isotherms of a nonionic (n-octyltetraoxyethylene, C(8)E(4)) and a cationic (cetylpyridinium chloride, CpCl) surfactant on silica gel are presented for different temperatures. The measured values are fitted with the Gu equation. From the generalized Clausius-Clapeyron equation or multicomponent adsorption, simplified equations are derived for the special cases treated in this contribution. The validity ranges of these equations are discussed. The differential molar adsorption enthalpies are determined from the fitted isotherms. We find that the adsorption of the nonionic surfactant is endothermic while that of the ionic surfactant is exothermic. It is shown that the electrostatic contribution of the diffuse double layer to the enthalpy of adsorption of an ionic surfactant is always negative. Advantages and limitations of the indirect method are discussed. The comparison of the indirectly determined enthalpies with directly (i.e., calorimetrically) measured enthalpies will be presented in the second part of this series.