Can one Calculate Fixed and Variable Cost From TC and Quantity Alone?
As said in my comment, 


  The fixed cost is usually defined as the cost when quantity is equal to zero, and the variable cost as the total cost minus the fixed cost.


Hence, if $TC(q)$ is the total cost for the given level of quantity $q$, then $FC=TC(0)$ is the fixed cost, which is a constant independent of $q$; and  $VC(q)=TC(q)-FC$ is the variable cost.

For example, if $TC(q)=10+q$, then $FC=TC(0)=10$ and $VC(q)=TC(q)-FC=q$.