Given the equations \(a^2 + b^2 = 16\) and \(2ab = 7\), we need to find the possible values of \(a - b\). 

Let's solve for \(a\) and \(b\) from the second equation \(2ab = 7\): \[ab = \frac{7}{2}\] Now let's consider the expression \((a - b)^2\): \[(a - b)^2 = a^2 - 2ab + b^2\].

Substitute the values of \(a^2 + b^2\) and \(2ab\) into the expression: \[(a - b)^2 = 16 - 2 \cdot \frac{7}{2} = 16 - 7 = 9\] 

Taking the square root of both sides: \[|a - b| = \pm 3\] This means that \(a - b\) can be either 3 or -3.