Cosmic rays in the inner solar system are subject to deflection by both the geomagnetic and interplanetary magnetic fields, and simultaneously interact with the Sun's photosphere resulting in the production of gamma rays. This phenomenon can be studied by observing the deficit ("shadow") in the cosmic ray flux from the direction of the Sun and searching for an excess photon signal above the isotropic background. The High Altitude Water Cherenkov (HAWC) Observatory in Mexico has been taking data on the solar disk at TeV energies since the end of 2014. We present our first efforts to estimate the luminosity of TeV gamma rays from the Sun which can be used to place limits on the production mechanisms, including astrophysical processes and beyond the standard model predictions.