Which two hormones are responsible for the regulation of kidney function? How do these hormones work?

There are 3 mechanisms for kidney function

The first 2 increase action of kidneys and the 3rd one decreases the action of kidneys

1. Renin-Angiotensin mechanism:

A fall in glomerular blood flow causes release of renin hormone via Juxta-Glomerular cells.

The renin hormone converts Angiotensin I into Angiotensin II, which is a powerful vasoconstrictor.

It constricts the blood vessels to increase the glomerular blood flow.

The Angiotensin II also causes release of Aldosterone from the adrenal cortex, which causes reabsorption of Na+ and water from distal parts of tubule.

This also leads to an increase in blood pressure and GFR

Illustration:

2) Anti-Diuretic hormone mechanism;

Hypothalamus releases ADH (also called as vasopressin) from neurohypophysis.

It facilitates water reabsorption from the latter part of the tubule.

It can also affect kidney function via its effects on blood vessels.

This increases the blood pressure due to which GFR increases.

3) Anti-Natritretic factor:

An increase in blood pressure causes the heart to release Anti-Natritretic factor.

It is a vasodilator which dilates the blood vessels, hence effectively decreasing the blood pressure and hence counters the Renin-Angiotensin mechanism.

Hope this helps

PS: GFR and Glomerular blood flow are the same thing.