We developed a unique model for exciton in monolayer medium with an effective dielectric constant Eeff (in which the monolayer material is placed on a substrate such as fused silica glass or SiO2 in experiments). Our model was based on an exact solution of the corresponding fully-covariant two-body Dirac-Coulomb type equation. For singlet quantum state of a static electron-hole pair in such a medium, we obtained a non-perturbative frequency spectrum composed of real and imaginary parts. We obtained explicit expressions for practical calculations of binding energy and decaytime of such a system. The results show that one can actively tune both binding energy and decaytime of an exciton during photo-excitation experiments by adjusting the value of Eeff. We think that our calculations and approaches eliminate cross-talk in the literature and explain the discrepancy between experimental results of binding energy of an exciton for different substrates.