LeetCode 494 Target Sum - Problem Statement

Given an array $nums$ and a target, assign + or - to each number so they sum to target. Return the count of ways to do this. For example, with $nums = [1, 1, 1, 1, 1]$ and target $= 3$, there are $5$ ways. This looks like a different problem entirely. You're assigning signs, not selecting subsets.

But there's a clever transformation hiding here. Before reading the solution, try this: if you call the numbers with + signs "$P$" and numbers with - signs "$N$", what equations can you write?