but the question is how to explain to your boss (controller)?
I think those differences were there for a long time before you joined this company. But nobody solved them or they did not want to do it. Now you are a new employee (just one month), so the controller pushes you to solve those differences.
If I were you, I will write down every detailed step to show to the controller and tell him or her how to solve each difference and what is the effect of the adjusting entries. Those differences absolutely will affect P/L accounts.
Make a long report to your controller and explain every detailed step/effect, which will make your controller know you totally understand your work and system. You are much better than previous accountants.