'Each' versus 'both'

A reader asks,

What is the correct usage for each and both? Example:
You and I both know what it’s like.
or
You and I each know what it’s like.

Each is singular. In relation to a group, it means “all of any number, considered individually.” Examples of usage:

Each child in the school has been vaccinated against smallpox.
When groups of individuals join together in business partnerships, each member of the partnership becomes bound by basic legal duties. 

Both is plural. It refers to two of something. Examples of usage:

Both men are Nobel Prize winners.
Walther’s lectures were both informative and entertaining.

When speaking of two people, both is usually the more appropriate choice. The only reason to use each when speaking of two people/things would be to emphasize the individuality of separate acts or to avoid ambiguity. Consider the following sentences:

1. Jack and Bill share a room. Both are responsible for cleaning half.
2. Mr. Jones gave both his daughters a dog.
3. Both of us received a letter this morning.

Most listeners would understand the first sentence to mean that each boy is responsible for one half of the room. Sentence three might be understood to mean that each of the two received separate letters. Sentence two is definitely ambiguous: Did each daughter receive a dog of her own, or did both daughters receive one dog to share? The following revisions would prevent misunderstanding:

1. Jack and Bill share a room. Each is responsible for cleaning half.
2. Mr. Jones gave each of his daughters a dog.
3. Each of us received a letter this morning.

In the reader’s question, the first example is correct: “You and I both know what it’s like.” The second example presents an impossibility of agreement: “You and I each know what it’s like.” The subject “You and I” is plural and requires the plural verb know. The word each, however, is singular and would require the singular verb knows.

Source: dailywritingtips.com