east coast of Middle earth
 

The numenoreans were great mariners, and they ventured to the far south, several hundred miles further south than the Havens of Umbar, but what i wonder is this; Is it possible that the Numenoreans rounded the cape of Ormal, where once the great lamp of the south was located and explored the eastern coasts of Middle-earth. Has Tolkien stated it somewhere? I find it very interesting, and the question has bothered my brain a while now.

When the Blessed Isles were separated from the rest of Middle-earth, The Silmarillion describes that mariners who tried to sail to Aman only rounded the Earth, and came back again.
It is also very likely that some Numenorean mariners sailed around the Cape of Ormal, and created some Black Numenorean settlements in the East and South.

that makes sense because the easterlings would have payed tribute so the numenoreans would have made settlements.

I think somewhere in the Unfinished Tales or The Lost Road it says that some of the ships that Elendil was commanding after the fall of Numenor were blown completely around Middle-earth (or at least that's what I think it said), so at least one of his ships may have landed there.

In the Akalabêth it is stated that they sail round the south of Middle-Earth:
Respectfully
Findegil