"애" is a noun meaning "a kid" or "love(愛)" while "에" is similar to a preposition like "to", "on", "in" or "at" in English. "태양애" doesn't make sense, it should be "태양에 (대한)" As to "에", 에밀리에게 = To 에밀리 은행에 가다 = to go to the bank 탁자위에 있다 = It's on the table. 나는 2000년에 태어났다 = I was born in 2000 나는 언제나 6시에 일어난다 = I get up at 6 am. As for "애", 나는 애가 둘 있다 = I have got two kids. (here, "애" is short for "아이- kid") 애국심(愛國心) = the love of your country (愛-love, 國- a country, 心-feeling) 애인(愛人) = a person who you have got a romantic relationship with like bf or gf. (愛- love, 人-a person) \^o^/

Pascal's answer is great. I am just answering about its pronounciation. 에 of 에밀리(Emily) sounds 'E' as in 'End' 애 of 태양(Taeyang) sounds 'A' as in 'And' even though we write it 'AE' for convenience.