Thank you for the link. My wife left Denmark 35 years ago and does not recall the use acents. Languages change.
Because the first one is an article and the second is a number. en = a ; én = one. But generally en is one too
en mand = a man ; én mand = ONE man: But en mand to kvinder works too : one man 2 women
It is not mandatory to use the accented letters é, ét. It is if you want to insist ( or emphazise ??) on the fact that it is a number and not an article
In the sentence above there is really no reason to use it except for educational purpose