The JAA expect you to use
LSS = 38.94 time the square root of the Absolute Temperature.
And
Mach No = TAS / LSS
So working backwards
LSS = TAS / Mach = 499 / .84 = 594.047619
Dividing by 38.94 give Square root of absolute temp = 15.25546017
Squaring this gives absolute temp = 232.729065
subtracting 273 gives -40.27093497 degrees C