how to reply email to selected cqndidate?

I have accidentally sent another appointment letter to a candidate. As there is a difference in salary of $600, this candidate is asking why she is paid less when both are the same designation. I did told her that same position but there is differences in salaries for different candidates, depending on experience. She replied that she believed she has relevant and more experience for the position. And she is taking her leave and unpaid leave to work for this project. She doesn't take my explanation.

I know that i've made a big mistake by sending the wrong appointment letter out, but i don't want to lose my job. I wish to clear this matter without telliing my boss. Can someone tell me how should i reply the email? Thanks a million