Symmetry energy quantifies the changes in nuclear energy when isospin grows away from zero. Knowledge of the symmetry energy is critical when extrapolating from nuclei to neutron stars. Charge invariance of nuclear interactions implies that the dependence of energy on isospin is primarily quadratic. Relying on the charge invariance, we examine nuclear excitation energies to the isobaric analog states of ground states of other nuclei in the same isobaric chain. In this fashion we are able to extract symmetry-energy coefficients on a nucleus-by-nucleus basis. The coefficients turn out to have a strong mass dependence that can be tied to different contributions from different densities in nuclei with different mass. In consequence, we are able to deduce constraints on the symmetry energy in nuclear matter as a function of density. The deduced constraints are narrow at subnormal densities, but spread out at normal density and above. Simultaneous analysis of elastic and quasielastic charge-exchange reactions may help narrowing the constraints. Finally, prospects to constrain the symmetry energy directly at supranormal densities using charged pion yields are discussed.

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