Solvation dynamics in liquid water is addressed via nonequilibrium energy-transfer pathways activated after a neutral atomic solute acquires a unit charge, either positive or negative. It is shown that the well-known nonequilibrium frequency shift relaxation function can be expressed in a novel fashion in terms of energy fluxes, providing a clear-cut and quantitative account of the processes involved. Roughly half of the initial excess energy is transferred into hindered rotations of first hydration shell water molecules, i.e., librational motions, specifically those rotations around the lowest moment of inertia principal axis. After integration over all water solvent molecules, rotations account for roughly 80% of the energy transferred, while translations have a secondary role; transfer to intramolecular water stretch and bend vibrations is negligible. This picture is similar to that for relaxation of a single vibrationally or rotationally excited water molecule in neat liquid water, although solvation relaxation is more nonlocal. In addition, we find a remarkable independence of the main relaxation channels on the newly created charge's sign. Although the methodology is applied here to the simplest solute case, the approach is rather general, and it should be at least equally useful in more realistic and complex scenarios.