Many languages, such as German (and Spanish), have "Sie" (you-formal) as a formal version of you. One can say use "Mr." and "Mrs.", but in a thank-you note / email, there is no formal word for English you can use to address your speaker. How does one get around it, to sound as proper as possible?
English does have a formal you: "You", for both singular and plural.
What is missing in most modern English is the informal or familiar you: Thee or Thou. Those forms are preserved for some uses, notably Christian prayers. We may address God as Thee because we feel as close to Him as a child to a father.
Some English speakers still use thee and thou. My father was born in the 1920s into a Quaker family. Within the family, he would say, "What thinkest thou?"
At one point there were formal and informal second person pronouns (informal: thou, thee, etc; formal: you, ye, etc.) However, "[b]y the late seventeenth century you had become normal in almost all contexts and thou and thee were limited to the Bible and religious use, the Quakers, and regional dialects" according to the OED Blog. (More on this can be found here.)
Thus, the most formal second person (singular and plural) pronoun is you (in contrast, there are currently several widely-used informal second person pronouns in different regions such as "y'all" and "you guys"). You can see you used in examples of letters/emails in pretty much any source you pick up. Here's an example from a book (Technical Communication, page 369) I happen to own (emphasis added):
Dear Mr. Larsyn:
As steady customers of yours for over 15 years, we came to you first when we needed a quiet pile driver for a job near a residential area. On your recommendation, we bought your Vista 500 Quiet Driver[...]
Jack Robbins, President
Use of "you" can create an informal tone in some types of writing, such as essay writing, documentation, or academic writing. In other words, writing which is not addressed to anyone where it would make sense to use "one" instead of "you" or rewrite things entirely.
And of course, there are other (unrelated) strategies to make writing more (or less formal), such as not using contractions.
It’s not true that English has no word that you can use to address someone formally. Indeed, it has at least two, depending on gender. They simply are not personal pronouns.
The tu–vous distinction is best implemented in English by addressing your interlocutor as sir or ma’am (or sometimes madam or miss) used vocatively as a noun of direct address.
Would you like ice in your whiskey, sir?
Why thank you, madam, that would be delightful!
It’s that extra word that makes it formal, as you might do with their full name Mr Smith or Mrs Jones, without either having to know it or to repeat it. The sir or ma’am stands in for the full formal name.
But if you talk like this all the time, people will think you’re very stand-offish. After all, you aren’t always addressing a police officer you’re trying to talk out of arresting you, or speaking solicitously to a well-heeled customer at some ritzy high-street shop.