The real wordsTheory
The identity, in three lines
Start from national income accounting, all in real terms.
Y = C + I + (X - M)
Let A = C + I (domestic absorption)
Let B = X - M (the trade balance, or foreign balance)
Then Y = A + B
and Y - A = B
Read the last line aloud: domestic production minus domestic absorption equals the trade balance. It is an identity, so it is true always, in every economy, whatever the exchange rate.