IELTS Letter topic: An explanation for the boss

During the interview I estimated fifteen days as the amount of time needed for me to finish my activities at my current job and start at your company, but due to the fact that I got sick for the last whole week and was not able to work, I could not finish my tasks and will need another week to do so. If necessary, I can provide  you a copy of the letter from my doctor informing that I had to stay at home and under medical care during that week.

I feel responsible for the pressure my delayed start may have created on the company, and I am going to work harder until everything is back to normal. To clear the backlog created by my late start, I can work two additional hours every day until I catch up, either coming in early or leaving late. 

I sincerely apologize for the inconvenience and hope this will not affect our relationship. If I am expected to present any other form of proof or talk to someone else in the company, please let me know.

Faithfully yours,
Leo Gomes