\[(a + ib)^2 = 7 + 24i \]

If \(a\) and \(b\) are integers satisfying the equation above, then find the value of \( |a| - |b| \).

\(\)

**Notation:**

- \(i = \sqrt{-1}\) is the imaginary unit.
- \(| \cdot |\) is the absolute value function.

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