We have derived the non-linear relationship between the reaction energies and activation energies of a reaction set, presenting a framework that offers insights beyond Bell-Evans-Polanyi relationships and Marcus equation. The derivation is grounded in a formulation stemming from the principle of microscopic reversibility, with an exponential dependence on the energies, and otherwise minimal assumptions about the reactions themselves. Consequently, the observed Brønsted slopes and intercepts of the linear approximations of a system constitute local descriptors, dependent on the underlying parameters and the studied thermodynamic range. The full non-linear understanding allows global comparisons between very different ranges of reaction energies and reaction families. We expect that factors that affect the sensitivity of energy barriers to the reaction energies to correlate strongly with the parameters governing the non-linear relationship, and therefore only indirectly with the local slopes and intercepts.