difference
The difference of two numbers $a$ and $b$ is a number $d$ such that
$$b+d=a.$$ 
The difference of $a$ (the minuend) and $b$ (the subtrahend) is denoted by $ab$.
The definition is for the elements $a,b$ of any Abelian group^{} (e.g. of a vector space^{}). The difference of them is always unique.
Note 1. Forming the difference of numbers (resp. elements), i.e. subtraction, is in a certain sense converse to the addition operation:
$$(x+y)y=x$$ 
Note 2. As for real numbers, one may say that the difference between $a$ and $b$ is $ab$ (which is the same as $ba$); then it is always nonnegative. For all complex numbers^{}, such a phrase would be nonsense.
Some

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$b+(ab)=a$

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$ab=a+(b)$

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$(ab)=ba$

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$n(ab)=nanb\mathit{\hspace{1em}}(n\in \mathbb{Z})$

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$aa=\mathrm{\hspace{0.33em}0}$
Title  difference 
Canonical name  Difference 
Date of creation  20130322 17:33:35 
Last modified on  20130322 17:33:35 
Owner  pahio (2872) 
Last modified by  pahio (2872) 
Numerical id  16 
Author  pahio (2872) 
Entry type  Definition 
Classification  msc 20K99 
Classification  msc 00A05 
Classification  msc 11B25 
Related topic  VectorDifference 
Related topic  SetDifference 
Related topic  Multiple 
Related topic  GeneralAssociativity 
Related topic  Quotient^{} 
Related topic  DifferenceOfVectors 
Defines  minuend 
Defines  subtrahend 