We performed Cu {it K}-edge X-ray absorption fine structure measurements on T-type La$_{1.8}$Eu$_{0.2}$CuO$_4$ (LECO) and Nd$_2$CuO$_4$ (NCO) to investigate the variation in the electronic state associated with the emergence of superconductivity due to annealing. The X-ray absorption near-edge structure spectra of as-sintered (AS) LECO are quite similar to those of AS NCO, indicating that the ground state of AS T-type LECO is a Mott insulator. We found a significant variation of the electronic state at the Cu sites in LECO due to annealing. The electron density after annealing ($n_{rm AN}$) was evaluated for both superconducting LECO and non-superconducting NCO and found to be 0.40 and 0.05 electrons per Cu, respectively. In LECO but not in NCO, extended X-ray absorption fine structure analysis revealed a softening in the strength of the Cu-O bond in the CuO$_2$ plane due to annealing, which is consistent with the screening effect on phonons in the metallic state. Since the amounts of oxygen loss due to annealing ($delta$) for LECO and NCO are comparable with each other, these results suggest distinct electron-doping processes in the two compounds. That electron-doping in NCO approximately follows the relation $n_{rm AN}=2delta$ can be understood if electrons are doped through oxygen deficiency, but the anneal-induced metallic nature and large $n_{rm AN}$ of LECO suggest a variation of the electronic band structure causes self-doping of carriers. The origin of the difference in doping processes due to annealing is discussed in connection with the size of the charge transfer gap.
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