  In this paper we are interested in the study of a two-phase problem equipped
with the $\Phi$-Laplacian operator
  $$ \Delta_\Phi u \coloneqq \mbox{div} \left(\phi(|\nabla u|)\dfrac{\nabla
u}{|\nabla u|}\right),
  $$
  where
  $\Phi(s)=e^{s^2}-1$ and $\phi=\Phi'$. We obtain the existence, boundedness,
and Log-Lipschitz regularity of the minimizers of the energy functional
associated to the two-phase problem. Furthermore, we also prove that the phase
change free boundaries of the minimizers possess a finite perimeter.
