If you want to strain the grey matter a bit, refer to any standard undergrad aerodynamics text .. in essence, the story is
M = TAS/local speed of sound
where local speed of sound, a
a/a0 = SQRT (T/T0)
where subscript 0 indicates standard sea level values and T is absolute (Kelvin or Rankine),
eg a0 = 661.48 kt and T0 = 288.15 K = 15 C
Rearranging for TAS
= M * a
= M * a0/SQRT(T0) * SQRT(T)
Substitute for whatever system of units is your cup of tea .. add a few unit conversion factors to taste and you end up with the sort of equation you are looking for .. something along the lines of
For
TAS kt
OAT C
= M * 661.48 / SQRT(288.15) * SQRT(273.15 + C)
= 38.97 * M * SQRT(273.15 + C)
(assuming I haven't made any numeric errors along the way .. )