So then "Een" can be both "A" and "An" depending on the situation? I wish they would have clarified this in the beginning so that I wouldn't have gotten this wrong thinking that they just made an error in wording.
The meaning of a and an is exactly the same, the only difference is that before a vowel sound an is used in English, and before a consonant sound a is used in English. In Dutch there is no such distinction and een is used regardless of the word that follows.
"A apple" is incorrect English. The indefinite article "a" is changed to "an" if it is followed by vowel.
"An apple" - "an" is used when the next word begins with a vowel sound. "an hour", "a uniform".