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How to calculate the solar day from sidereal day and sidereal orbital period?

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I know the orbital period of my planet and the rotational period of my planet. Now how do I calculate the solar day? It would only be a small difference to be sure, but do remember that if we didn't use solar days instead of sidereal days, noon would be 12:00 AM in July and 12:00 PM in January.

EDIT: It was staring at me in the face. If the phase is half a rotation period for half a year, it means the solar day is exactly one day slower than a sidereal day and it's a simpler math problem.

EDIT2: As far as I can tell the formula is the following:

(P/(Y-P)) + P = D

Where P = Sidereal Rotational Period, Y = Sidereal Orbital Period, and D = Solar Rotational Period.

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This post was sourced from https://worldbuilding.stackexchange.com/q/84577. It is licensed under CC BY-SA 3.0.

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