[tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex]
[tex] {a}^{2} - {b}^{2} = 24[/tex]
[tex]a - b = 2 \sqrt{2} [/tex]
[tex]24 = 2 \sqrt{2} (a + b)[/tex]
[tex]a + b = \frac{24}{2 \sqrt{2} } [/tex]
[tex]a + b = \frac{12}{ \sqrt{2} } [/tex]
[tex]a + b = \frac{12 \sqrt{2} }{2} [/tex]
[tex]a + b = 6 \sqrt{2} [/tex]