* "an" is a definite article. It's used before a singular noun that starts with a vowel sound (like "argument").
* Adjectives describe nouns. They tell us more about the noun. For example, in the sentence "Jane and Todd were involved in a heated argument concerning the car," the word "heated" is an adjective because it tells us more about the argument.
The sentence you provided lacks a word that directly describes the argument itself.