To isolate c means to separate it completely on one side of the equals sign.
To isolate variables, you apply opposite operations.
In E = mc², m and c are being multiplied together. To separate them, you divide by the variable you want to get rid of. However, you must do this to both sides of the equation always. Whatever you do to one side of the equation you must do to the other side as well. This is so the equation remains true.
Since we want to isolate c, we'll start by dividing both sides by m.
E = mc²
E/m = mc²/m
E/m = c² -- The m's cancel as 1
Now we have c squared. The opposite of squaring something is taking its square root. Take the square root of each side.
E/m = c²
√(E/m) = √(c²)
√(E/m) = c -- Opposite operations cancel each other out
