Hearing exercise - how do I know if it's et or ett? Couldn't it be the first form and translate to: Add an egg?
Also, in English "add one egg" and "add an egg" are synonymous. It should be an acceptable answer.
Actually they should be pronounced differently. "en/ei/et" cannot (usually) be stressed, and are in practice always unstressed. "Én/ éi/ ett" on the other hand are always stressed. In the audio here it sounds unstressed to me. There are a few fixed expressions where it is allowed to write "en/ei/et" although they are stressed, as in constructions like "en/ei/et av..."+++
"et" and "ett" meaning "a/one" have the same vowel length, the only difference is stress, as described above. There is another word, "et", which is the imperative of the verb "ete" (eat), and that one does indeed follow the rules you describe, which are usually followed.