How to solve this? $a,b\in R, a+\ln{a}=2, \ln{(1-b)}=b+1$, show value of $a+b$.

Question

How to solve this? $a,b\in \Bbb R, a+\ln a=2, \ln (1-b)=b+1$, show value of $a+b$.
Notice that $\ln (1-b)+(1-b)=2$, we have $1-b=a$.
But I don't understand the reason to do this. Why do I have to change the form of the 2nd equation? Is there any idea? Or other methods to calculate the sum of $a$ and $b$?