(It's assumed that we use the income method.)
GDP is supposed to include all incomes received on territory of given country, no matter if receivers of income are citizens or not. So incomes of foreigners in given country (I will write them as FH, stands for "foreigners here") are included into GDP, but incomes of citizens abroad(I will write them as CA, stands for "citizens abroad") are NOT included. GDP=Wages+Rent+Interest+Profits+Sales Taxes+Deprecation+Net Foreign Factor Income. For sake of simplicity I will replace "Wages+Rent+Interest+Profits+Sales Taxes+Deprecation" with "A". The formula can be rewritten as GDP=A+NFFI
As for Net Foreign Factor Income, it's the difference between income that citizens of given country earned abroad and income that foreigners earned in given country. Or in my notation, NFFI=CA-FH. Considering this, the formula of GDP can be rewritten as GDP=A+CA-FH. But it's wrong! This way we will include incomes of citizens aborad and exclude incomes of foreigners in given country, but it should be reverse of that, we should include incomes of foreigners in given country and exclude incomes of citizens abroad. In short, it should be GDP=A-CA+FH. We can get this effect either if we change how NFFI is calculated (NFFI=-CA+FH would do the trick) OR if we substracted NFFI from A, instead of adding it.