For two-center Lennard-Jones molecules with embedded point dipole (2CLID-molecules) a hybrid equation of state for the Helmholtz energy F-2CLID is constructed as the sum of the Helmholtz energy F-2CLJ for nonpolar two-center Lennard-Jones molecules and the dipolar contribution to the Helmholtz energy F-D, F-2CLJD = F-2CLJ + F-D. For pure fluids, predictions from this equation for the thermodynamic data of the homogeneous phase and for the vapour-liquid phase equilibria show good-to-excellent agreement with simulation data. To study deviations from the corresponding states theorem, acentric factors are calculated, and isoacentric curves are given as a function of the molecular elongation and the dipole strength. The equation is then used for a description of the real fluids R22 and R152a. Finally, it is shown that properties of model mixtures are also well predicted by using an appropriate mixing rule.