The problem does not specify a right triangle... so we have to work with the law of sines, law of cosines and the fact that the sum of the angles is 180 degress.

A + B + C = 180

a/(sin(A)) = b/(sin(B)) = c/(sin(C))

c^2 = a^2 + b^2 - 2ab(cos(C))

We know that c = 26

We state that b = a - 14

26^2 = a^2 + (a-14)^2 - 2a(a-14)(cos(C))

26^2/(cos(C)) = a^2 + a^2 - 28a + 14^2 - 2a^2 - 28a

= 56a + 14^2

so

a = (26^2/(cos(C)) - 14^2) / 56

...and from there you're on your own because the fact that this is not a right triangle means this will take a fair amount of careful substitution!