"We're both" or "both of us"?

For example:

• We're both 20.

• (The) both of us are 20.

I don't mean to include the person I'm talking to. Which one is more appropriate?

Solution 1:

Both

We are twenty

and

Both of us are 20

are grammatically correct and appropriate. Using the option with the sounds terribly old fashioned and non-idiomatic.

The hearer understands that 'both' does not include him/her by the context and discernment of the speaker's intention.