Confused about the functioning of a QRE1113 reflectance sensor
This is a simple Ohm's Law calculation.  You know that the desired Vout is 1.4V so we need to drop 5 - 1.4 volts across R2 when 0.36 mA is flowing.  So the answer would be:
R = V/I = (5 - 1.4)/0.00036 = 10K Ohms
What's happening with R1 is not related.