Limits and Continuity · Hard problem

Two sensors report $\displaystyle\lim_{x\to5}f(x)=a$ and $\displaystyle\lim_{x\to5}g(x)=b$ for unknown numbers $a<b$, but a technician only recorded the combined readings $\displaystyle\lim_{x\to5}\bigl(f(x)+g(x)\bigr)=10$ and $\displaystyle\lim_{x\to5}\bigl(f(x)\cdot g(x)\bigr)=24$. Can $a$ and $b$ still be pinned down separately from this? Find $b-a$.