A new theory of solutions, the method of energy representation, is introduced by adopting the solute-solvent interaction energy as the coordinate of distribution functions. The density-functional theory is formulated over the energy coordinate, and an approximate functional for the solvation free energy is given in terms of energy distribution functions in the solution and reference solvent systems. The method of energy representation greatly expands the scope of solution theory and is amenable to supercritical fluid, flexible molecules with intramolecular degrees of freedom, inhomogeneous system, and quantum-mechanical/molecular-mechanical (QM/MM) system. Through the combination with molecular simulation, the functional for the solvation free energy is demonstrated to perform well for nonpolar, polar, and ionic solutes in water over a wide range of thermodynamics conditions, with drastic reduction of the computational demand compared to the standard free-energy perturbation and thermodynamic integration methods. As an application to inhomogeneous system involving flexible species, the molecular binding into micelle and membrane is analyzed by treating micelle and membrane as a mixed solvent system consisting of water and amphiphilic molecule.