I am writing an email to my Manager regarding vacation
I still have 10 days vacation days left. I would like to take May 28 to June 1. I plan to be out of town and I need to book my air ticket by end of next week. I hope you will approve my vacation plan.
I'd suggest "my plane ticked by the end of next week."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.