Thabit and Williams Numbers Base b as a Sum or Difference of Two g-Repdigits

We investigate cases where Thabit and Williams numbers in base b can be expressed as the sum or difference of two g-repdigits. For specific values of b and g, we describe parametric solutions yielding infinitely many solutions for some equations and establish upper bounds for the parameters of the remaining finitely many solutions. As an illustration, we also provide a complete solution for some equations.