The primary entry point to the eos module is through the routine eosDT_get. Broadly, one provides the density, temperature and full composition information. Then the EOS returns its main set of results, their temperature and density derivatives, and the composition derivatives of a small subset of the results.
../../../eos/public/eos_lib.f90
The underlying EOS is in a density-temperature basis, but if one has only density or temperature, there are search interfaces (eosDT_get_Rho and eosDT_get_T) for searching for the other, given some another known EOS quantity (e.g., lnE).
../../../eos/public/eos_lib.f90
For legacy reasons, there is also an eosPT_get entry point. (The same result could ultimately be achieved via eosDT_get_Rho.) Internally, this is also implemented as a root-find using the standard density-temperature EOS.
../../../eos/public/eos_lib.f90