Four roots

Algebra Level 4

The roots of the equation $\large x^4 - 10x^3 + 26x^2 - 10x + 1 = 0$ are in the form $\large a \pm b \sqrt{c}$ ; $\large d \pm \sqrt{e}$

Find $\large a + b + c + d + e .$

This problem is a part of the sets - 3's & 4's & QuEsTiOnS.