How to measure added voltage to my input?
Your diagram does not make much sense. 

Based on the equation, change Y from 0 to 1V and measure the change in the output voltage. 

Then you will have: \$ e + G = \frac{\Delta Z}{\Delta Y}\$ , provided Y stays constant. 

If there is no offset then 

\$X = \frac{Z}{e+G}\$ when Y = 0