Well I have the general Idea to get you started... To calculate the date from the number of nights you need to keep counting the days from the start date.

We know that January has 31 days, February 28 and so on... but February's number of days change according to leap years... So you need some function to check if the year is leap or not (you'll find plenty on the net)...

Keep on counting the days until you hit your new date... That's it...

Let me add that I'm sure there are better solutions (Usually when it comes to dates there could be some Math involved in it and you get a formula to solve your problem).

Good luck