L = { w | w ϵ (a,b)* and #a(w) - #b(w) ≤ 10}.
number of a's - number of b's <=10. it's an infinite language because there can be infinite number of a's and b's whose difference is less than 10.
for example a's=100, b's=95 or a's=10000, b's=9998 and so on..
It's an infinite language, So if it's a regular language then its complement should also be regular, as Regular languages are closed under complement operation. Suppose $L^{c}$ is the complement of L:
$L^{c}$ = { w | w ϵ (a,b)* and #a(w) - #b(w) >10}. which also a non-regular.
Hence L is a non-regular language.