The challenge provides us with an image that has 26 words paired with numbers. Think of each word as an equation, and all words together as a system of linear equations.
For example, the first pair is apple 453. This can be thought of as a + 2p + l + e = 453.
Each equation has infinite solutions, but together as a system they have 1 solutution. In the solution, a = 70, b = 35, etc. If you put them in alphabetical order, they will be the ascii values for the flag.
Use any tool to solve this. I chose to represent the systems of equations as sage matricies and have sage do some linear algebra to solve them.