How do I calculate the input voltage based on an ADC reading?
There are two possibilities here:


That the uC has a fully calibrated ADC with precision circuits and temperature correction.  In which case you just need to read through the 418 page *.pdf and find the relationship or ..
It is uncalibrated and you can only get an approximation.  SO that means that you have to calibrate the input vs. binary # ahead of time and hope it does not change with temperature too much.  Simply sweep the voltage on the pin, read it with a DMM and compare that to the ADC value. 


Since this is a high volume product with tight profit margins I suspect #2 is what you'll have to do.

Keep in mind that you also will have tolerances on the R18 and R19 it's looking more and more like you'll just have to calibrate it.  Of course this all depends upon precision needed.  You could possibly get away with just reading two values and fitting a straight line to those.  If \$D_1\$ is digital reading #1 corresponding to \$V_1\$ with the measured pair \$D_1\$, \$V_1\$ you simply:

\$V_x = \frac{V_2-V_1}{B_2-B_1}B_x+\frac{(V_1B_2-V_2B_1)}{B_2-B_1}\$

where \$B_x\$ is the new sample value.

Using your samples:"V1= 10V, V2= 12V; B1= 2023, B2= 2428, Bx= 2432"

We get V = \$ = \frac{2}{405}B_x + 0.0098 = 0.004938 B_x + 0.0098\$

\$V_X = 12.02 \$