Formulating an equation that represents the situation, we have:
1/2*x + 4 = 26 (x represents the initial number of stamps)
1/2*x = 26 - 4 (Subtracting 4 from both sides of the equation)
1/2*x= 22 (Subtracting)
x= 22 / (1/2) (Dividing by 1/2 on both sides of the equation)
x= 44 (Dividing fractions)
The answer is 44 stamps.