Measurements of the Coulomb excitation probabilities of the first ${2}^{+}$ state of $^{122}\mathrm{Te}$ and $^{128}\mathrm{Te}$ were carried out using back-scattered ions of $^{4}\mathrm{He}$, $^{14}\mathrm{N}$, $^{16}\mathrm{O}$, and $^{18}\mathrm{O}$. Quadrupole moments ${Q}_{{2}^{+}}$ and reduced transition probabilities $B(E2; {0}^{+}\ensuremath{\rightarrow}{2}^{+})$ were determined. The ${Q}_{{2}^{+}}$ deduced for the positive sign of the $2_{2}^{}{}_{}{}^{+}$ interference term are $\ensuremath{-}0.57\ifmmode\pm\else\textpm\fi{}0.05 e$ b and $\ensuremath{-}0.06\ifmmode\pm\else\textpm\fi{}0.05 e$ b for $^{122}\mathrm{Te}$ and $^{128}\mathrm{Te}$, respectively.[NUCLEAR REACTIONS $^{122,128}\mathrm{Te}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, ${E}_{\ensuremath{\alpha}}=8\ensuremath{-}10$ MeV; $^{122,128}\mathrm{Te}$($^{14}\mathrm{N}$, $^{14}\mathrm{N}$'), ${E}_{{14}_{\mathrm{N}}}=32\ensuremath{-}37$ MeV; $^{122,128}\mathrm{Te}$($^{16}\mathrm{O}$, $^{16}\mathrm{O}$'), ${E}_{{16}_{\mathrm{O}}}=30.5\ensuremath{-}42$ MeV; $^{122}\mathrm{Te}$($^{18}\mathrm{O}$, $^{18}\mathrm{O}$'), ${E}_{{18}_{\mathrm{O}}}=34\ensuremath{-}35$ MeV; measured $\ensuremath{\sigma}({E}_{\ensuremath{\alpha}},{E}_{{\ensuremath{\alpha}}^{\ensuremath{'}}})$, $\ensuremath{\sigma}({E}_{{14}_{\mathrm{N}}},{E}_{{14}_{{\mathrm{N}}^{\ensuremath{'}}}})$, $\ensuremath{\sigma}({E}_{{16}_{\mathrm{O}}},{E}_{{16}_{{\mathrm{O}}^{\ensuremath{'}}}})$, $\ensuremath{\sigma}({E}_{{18}_{\mathrm{O}}},{E}_{{18}_{{\mathrm{O}}^{\ensuremath{'}}}})$. $^{122,128}\mathrm{Te}$ deduced ${Q}_{{2}^{+}}$, $B(E2,{0}^{+}\ensuremath{\rightarrow}{2}^{+})$. Enriched targets.]