The difference between an exponential number and a power of 10?

Exponential numbers are in the form ax where a and x are real numbers. A power of 10 is any number in the form 10x. By definition this is an exponential number. If by "an exponential number" you mean THE exponential number, e, then the difference lies in the value of the base. e is a transcendental number (just like pi) with a value of approximately 2.71818182859045235... Just like pi, this decimal theoretically does not terminate and does not repeat i.e. goes on for an infinite number of places. e is known as the "natural base" because it appears in many natural structures from logarithms to compound interest to complex numbers.