Every Real number is expressible in terms of differences of two transcendentals Is it true that for every real number $x$ there exist transcendental numbers $\alpha$ and $\beta$ such that $x=\alpha-\beta$?
(it is true if $x$ is an algebraic number). 

If $x$ is algebraic and $a$ is transcendental, then $x+a$ is also transcendental and $(x+a)-a=x$. If $x$ is transcendental, then $2x$ is also transcendental and $2x-x=x$.
