We have investigated the effects of magnetic Ni and nonmagnetic Zn impurities on the superconductivity in undoped T-La$_{1.8}$Eu$_{0.2}$CuO$_4$ (T-LECO) with the Nd$_2$CuO$_4$-type structure, using the polycrystalline bulk samples, to clarify the pairing symmetry. It has been found that both suppression rates of the superconducting transition temperature $T_mathrm{c}$ by Ni and Zn impurities are nearly the same and are very similar to those in the optimally doped and overdoped regimes of hole-doped T-La$_{2-x}$Sr$_{x}$CuO$_4$ with the K$_2$NiF$_4$-type structure. These results strongly suggest that the superconductivity in undoped T-LECO is of the $d$-wave symmetry and is mediated by the spin fluctuation.