The EPC runs in a standard Linux virtual machine and you have full root access to it.
So you can just link your C++ code to the Mathematica Kernel by LibraryLink or WSTP or RunProcess.
All you need is a compile (g++ or a commercial one) and you are good to go.
Since it is also possible to call Fortran code by either LibraryLink or through C by using the new standardized way (https://gcc.gnu.org/onlinedocs/gfortran/Interoperability-with-C.html) to call Fortran from C, it is also possible to call existing Fortran code from Mathematica (through WSTP). I have experimented along these lines some time ago and while a bit cumbersome to set up,
it just works fine (on Linux and even on Windows (even more cumbersome, but possible)).