te form + infinitive +noun

Question

In a song called "Tegami" I don't understand 宛てて+書く in

未来の自分に宛てて書く手紙なら

I wonder what's this rule and does this mean address(v) + write (v) or together make new meaning?

Answer 1

宛てて書く is not an idiomatic/compound verb. It's just two verbs, connected using the te-form.

宛てて is the te-form of the verb 宛てる (to address (a letter)), and this kind of te-form describes how or under what circumstances the second verb (書く) is done. In general, this type of V1 + て/で + V2 can be translated as "V2 (while) doing V1" or "V2 by doing V1".

Examples:

• 歩いて学校に行く go to school by walking / go to school on foot
• 包丁を使ってたまねぎを切る cut an onion using a knife
• 未来の自分に宛てて手紙を書く write a letter addressing the future self
• 注意して歩く walk while paying attention / walk with attention
• 遊んで過ごす live an idle life

See: て form and adverbial meaning

Answer 2

手紙 - A letter

書く手紙 - To write a letter

宛てて書く手紙 - To address and write a lettter

When you put it together with the rest of the lyrics:

未来の自分に宛てて書く手紙なら

If it's a letter written to myself in the future.... (next lines in the song finish the sentence)

And the verb form is yes, just て-form + the dictionary form, which joins two verbs.