TAS = EAS/root(sigma)
sigma = local density/std SL density
The normal standard (troposphere) atmosphere derivation leads to the relationship
sigma = theta^4.25588
theta = local OAT/std SL OAT (temps in absolute deg K = deg C +273)
These relationships should give you something very close to what comes out of your whizz wheel activities.
Try looking in any of the standard undergrad engineering texts on aerodynamics etc for the background if you want an arithmetic headache ....