Let's solve for the value of \(\frac{e + 3f}{f - 3e}\) given that \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\). We can start by cross-multiplying to get rid of the fractions:

(3e + f)(5) = (3f - e)(2)
15e + 5f = 6f - 2e
17e = f

Now, we can substitute this value of `f` into the expression for \(\frac{e + 3f}{f - 3e}\):

\(\frac{e + 3f}{f - 3e}\) = \(\frac{e + 3(17e)}{17e - 3e}\)
= \(\frac{e + 51e}{14e}\)
= \(\frac{52}{14}\)
= \(\frac{26}{7}\)

Therefore, the value of \(\frac{e + 3f}{f - 3e}\) is \(\frac{26}{7}\)