This study entails the fourth part of a global flare energetics project, in which the mass m_cme_, kinetic energy E_kin_, and the gravitational potential energy E_grav_ of coronal mass ejections (CMEs) is measured in 399 M and X-class flare events observed during the first 3.5 years of the Solar Dynamics Observatory (SDO) mission, using a new method based on the extreme ultraviolet (EUV) dimming effect. EUV dimming is modeled in terms of a radial adiabatic expansion process, which is fitted to the observed evolution of the total emission measure of the CME source region. The model derives the evolution of the mean electron density, the emission measure, the bulk plasma expansion velocity, the mass, and the energy in the CME source region. The EUV dimming method is truly complementary to the Thomson scattering method in white light, which probes the CME evolution in the heliosphere at r>~2R_{sun}_, while the EUV dimming method tracks the CME launch in the corona. We compare the CME parameters obtained in white light with the LASCO/C2 coronagraph with those obtained from EUV dimming with the Atmospheric Imaging Assembly onboard the SDO for all identical events in both data sets. We investigate correlations between CME parameters, the relative timing with flare parameters, frequency occurrence distributions, and the energy partition between magnetic, thermal, nonthermal, and CME energies. CME energies are found to be systematically lower than the dissipated magnetic energies, which is consistent with a magnetic origin of CMEs.