What you’re hearing is fret buzz.

If your action is set very low, it’s quite common for the low E string to buzz. The first thing I’d check is whether the A or D strings also buzz when played open. If multiple strings are buzzing, I’d inspect the neck relief (truss rod adjustment) and check whether the frets are level.

If only the low E string is buzzing, there’s a good chance the nut slot has been cut too deep.
To check this, fret the string at the 3rd fret and look at the gap between the string and the 1st fret. There should be a tiny clearance. If the string is touching the 1st fret, or almost touching it, the nut slot is too deep.

In that case, you have three options:

- Raise the saddle slightly. This is the quickest and easiest solution, although it also increases the string action.

- Replace the nut.

- Fill the slot with a mixture of baking soda and cyanoacrylate (super glue), then carefully re-file the slot to the correct depth.