Write an interactive program that repeatedly asks the user to input a number until "Enter" is hit. Your program should create a file named "numbers.txt" where all the numbers are written one below the other, and the last line should display the sum of all the input, after the string "The sum of your numbers is".
For example, if the user inputs 3, 5, 7, 10, -3, 5.2, then the file "numbers.txt" should contain:
3
5
7
10
-3
5.2
The sum of your numbers is 27.2

Note: The program should be written in the Python programming language!