Coulomb's Law from Gauss's Law

$\iint E\cdot dA=\frac{q}{{\epsilon }_0}$ (Gauss’s Law)

A uniform enclosure for a region would be a sphere. For a sphere, surface area = $4\pi r^2$ Assuming the surface enclosing the charge is a sphere,

$\iint E\cdot dA=E\cdot 4\pi r^2$

So, $E\cdot 4\pi r^2=\frac{q}{{\epsilon }_0}$

$⟹E=\frac{1}{4\pi r^2}\frac{q}{{\epsilon }_0}$

$⟹E=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}$