Algebrais a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables.
Subtracting a negative is the same as adding the equivalent positive. For example, subtracting minus 10 is the same as adding 10.
There are lots of different types of problems in algebra; you have to learn each type separately. For example, how to add similar expressions; how to multiply expressions; how to factor polynomials; how to solve equations; etc.