Given the sum of the first n terms of an arithmetic progression is \(S_n = n^2 + 8n\).

For the first term \(S_1\):

\(S_1 = 1^2 + 8 \times 1 = 9\)

Thus, the first term \(a = 9\).

For the second term \(S_2\):

\(S_2 = 2^2 + 8 \times 2 = 20\)

We know \(S_2 = a + (a + d)\), so:

\(20 = 9 + (9 + d)\)

\(20 = 18 + d\)

\(d = 2\)

Therefore, the first term is 9 and the common difference is 2.