Friendship with 2 different personality types

Just would like some advice on a "friendship", because I am not sure at the moment if youd call it that.

Its fairly newly established-bout 6 months. And I do like them, as a person, but from my point of view are becoming increasingly difficult to deal with. Having a friendship with a personality-type like this person is new to me.

I am of the quietly confident variety, loyal, and very trust worthy. It takes me time to build up friendships. I would definitely care about my friends. I know who they are. No bullsh*t.

This person has a lot of good qualities. Funny and exciting. But the world revolves around themselves. Ive never seen the like. I found it interesting at the start. But now its grinding me down.

Id given them a little gentle chat about 2 weeks ago saying look for the friendship to thrive etc (which is what I would like), I need to be included in conversation (when I say something about myself, its discounted).

Yesterday, after another day of them talking about themselves, I sort of blew up at them. They asked me after a full days conversation about themselves "how are you-Im not really interested but Ill ask anyways".

Is there any way to deal with a person like this? Am beginning to realise my needs arent being met in this "friendship" but the person will probably never change either.

So, does 2 different personality types = no friendship?