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Just think of addition and subtraction as directions on the number line. There are also several rules and properties that define how to perform these basic operations. To add integers having the same sign, keep the same sign and add the absolute value of each number. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite. Watch out! The negative of a negative is the opposite positive number.
So to accommodate subtraction, and to be able to represent amount owed by numbers, we extend the natural numbers to include the numbers 0 and the negatives of the natural numbers. This entire set of numbers, positive natural numbers, their negatives and 0 is called the set of integers, and is denoted by the letter Z. We can take any two members of Z and add them or subtract them and in either case get another member of Z. I know all that, but I am very rusty on actual additions and subtractions.