Help calculating Speed To Fly for headwind and tailwind

I am looking for the equations to determine the speed to fly for a
headwind or tailwind. I can calculate the the speed to fly for no
wind based on the polar from Equation V (Page 106, 1988 US Version) in
Reichmann. He gives a graphical method to determine the speeds for a
headwind or tailwind but I would like to translate this into an
equation.

I can do it by shifting the polar to the "true" ground speed, but then
I have to correct the predicted STF from the equation by adding or
subtracting the wind again. I'm not sure if this is the best way to do
it.

Anyone have a good set of equations or example of how to do this
simply?

Thanks,

Tim