Equation for Relative Humidity at a given Temperatur from Relative Humidity

Well that would give me the difference between intake and outtake but because humidity is temperaturecompensated a formula is needed

i need the intake relative humidity to be calculated with the outtake temperature (for each sensor the BSEC Bosch Library does exactly this but i need need to calculate from intake humidity and outtake temperature, so i know which relative humidity the intake air is gonna end with at the outtake sensor)