They're almost the same thing; they're both nouns. However, entry is usually used when 1) describing how a person joins a group with the same cause, such as a game or school
2) It can also refer to one's right to join something
Examples : 1) My entry into the football team was the best decision of my life
2) Sasuke was granted entry into the Akatsuki
(Excuse my anime reference 😅)
On the other hand, entrance is usually used to 1) refer to, say, a gate or a doorway (though entry can also be used, but rarely).
2) It is also used to describe a person's first appearance, probably in a book or music video
Examples: 1) The entrance to the gym is on the other side.
2) Millie's runway entrance was rather interesting.
I suggest you read more on these, though!