By definition

E.g

$f (x) = f (x+h) --------- \to(1)$

$\Delta f(x) =f(x+h)-f(x)$

$\Delta f(x) =Ef(x)-f(x)$

$\Delta f(x) =(E-1)f(x)$

$\therefore \Delta =E-1$

$\therefore E= 1+ \Delta ---------------- \to (2)$

Also

E.g

$f (x) = f (x + h)$

$f(x) +hf^1(x)\dfrac {h^2}{2!}f^1(x)+\dfrac{h^3}{3!}f^1(x) + ............$ Taylor series

$f(x) +hDf(x)\dfrac …