Given equations for the dew/bubble point curves, and given that pressure and enthalpy are known, can temperature and quality be calculated?

As mentioned, I have equations for both the dew and bubble point curves, T(P) or P(T) and also rho(T), rho(P).

I also know the actual pressure, and enthalpy of the liquid-gas mixture. Is this enough information to find the temperature and quality?

It seems as though using an energy balance or the lever rule might work, but I have not been able to figure it out so I’m looking for advice on this