The shift operator $E$ is defined as $E [f(x_i)] = f (x_i+h)$ and $E'[f(x_i)]=f (x_i -h)$ then $\triangle$ (forward difference) in terms of $E$ is
Forward difference operator(delta (D))
D(f(x)) = f(x + h) - f(x)
Shift operator , Ef(x) = f(x+h) = f(x+h) - f(x) + f(x) = (1 + D)f(x)
so E= 1 + D
gives D = E - 1