An approximate functional for the chemical potential of a solute in solution is presented in the energy representation. This functional is constructed by adopting the Percus-Yevick-like approximation in the unfavorable region of the solute-solvent interaction and the hypernetted-chain-like approximation in the favorable region. The chemical potential is then expressed in terms of energy distribution functions in the solution and pure solvent systems of interest, and is given exactly to second order with respect to the solvent density and to the solute-solvent interaction. In the practical implementation, computer simulations of the solution and pure solvent systems are performed to provide the energy distribution functions constituting the approximate functional for the chemical potential. It is demonstrated that the chemical potentials of nonpolar, polar, and ionic solutes in water are evaluated accurately and efficiently from the single functional over a wide range of thermodynamic conditions.