The Door Number

Eda and Ece are invited by Naz, who is a new neighbour in their housing. They accept the invitation and ask for the room number.

Naz replies as;

My room number is one of the following ten numbers:

43, 45, 36, 39, 23, 24, 26, 14, 15, 10

Then she whispers to Eda the tens digit of the number, and similarly, Ece learns the other digit. 

Eda says: "I don't know Naz's door number, but Ece, you also don't know."

Ece replies: "You are right, I didn't know, but now I know it."

Eda: "Hmm, then I also know what it is now."

What do you think is the door number?

I was asked this question by a colleague in a van during a trip, and we had quite a good time trying to solve it. I realized that it was a popular question on Turkish social media and forums a few years back. Unfortunately, I could not find the owner of the problem.