The Wigner Isobaric Multiplet Mass Equation (IMME) is the most fundamental prediction in nuclear physics with the concept of isospin. However, it was deduced based on the Wigner-Eckart theorem with the assumption that all charge-violating interactions can be written as tensors of rank two. In the present work, the chargesymmetry breaking (CSB) and charge-independent breaking (CIB) components of the nucleon-nucleon force, which contribute to the effective interaction in nuclear medium, are established in the framework of Brueckner theory with AV18 and AV14 bare interactions. Because such charge-violating components can no longer be expressed as an irreducible tensor due to density dependence, its matrix element cannot be analytically reduced by the Wigner-Eckart theorem. With an alternative approach, we derive a generalized IMME (GIMME) that modifies the coefficients of the original IMME. As the first application of GIMME, we study the long-standing question for the origin of the Nolen-Schiffer anomaly found in the Coulomb displacement energy of mirror nuclei. We find that the naturally-emerged CSB term in GIMME is largely responsible for explaining the Nolen-Schiffer anomaly. Introduction. The similarity of proton and neutron masses and approximate symmetry of nucleon-nucleon interactions under the exchange of the two kinds of nucleons lead to the concept of isospin [1,2]. At the isospin-symmetry limit, the charge-symmetry requires that the free proton-proton interaction v pp excluding the Coulomb force is equal to the neutronneutron v nn , while the charge-independence requires that the neutron-proton interaction v np = (v nn + v pp )/2 [3]. However, the nucleon-nucleon scattering data suggested that v nn is slightly more attractive than v pp , and v np is stronger than (v nn + v pp )/2 [4,5]. In real nuclear systems where manybody effects are important [6], isospin symmetry breaking has long been an active research theme connected to different subfields, for examples, in understanding the precise values of the Cabbibo-Kobayashi-Maskawa (CKM) mixing matrix elements between the u and d quarks [7,8], the changes in nuclear structure near the N = Z line due to charge-violating nuclear force [9][10][11][12], and the influence in nova nucleosynthesis [13].