I am in charge of distributing petty cash in the office I work. The other day I gave $100 to my non-jewish co-worker to pay for dinner for the office. The next day she gave me the receipt which was for $90 and she said she gave the delivery guy all the money I gave her assuming I had given her only $90. Then she said that she saw 4 twenty dollar bills and 1 ten dollar bill. According to my calculations, I am missing ten dollars. She offered to pay me the $10 if I’m positive that I actually gave her $100. What am I required to do according to halacha, without causing a chillul hashem?

There is no Chilul Hashem here. If you are certain about the case you should charge her with the 10$ and explain yourself clearly to your superiors. Rabbi Dov Lior