Soft matter systems, including polymers and proteins, experience structural changes under thermal, mechanical, or chemical stress. This study examines how the solvation of polyethylene glycol (PEG) in water is influenced by NaCl, balancing the well-known salting-out effect with potential ion-polymer interactions reminiscent of crown ethers. Using energy-representation theory, we compute solvation free energy changes via unidirectional and bidirectional estimators The bidirectional estimator, akin to Bennett Acceptance Ratio (BAR), captures the free energy relaxation between ensembles, revealing distinct thermodynamic contributions. Our findings indicate that the preferential binding coefficient changes linearly with salt concentration, maintaining a constant m-value contribution. This framework not only quantifies excess chemical potential shifts upon salt addition but also provides mechanistic insights by decomposing solvent-species and energy-domain contributions. These results enhance our understanding of salt-polymer interactions and their broader implications in soft matter thermodynamics.