JavaScript (Firefox), 80 bytes
solution=
a=>b=>[for(_ of(i=0,a))for(_ of(j=!++i,a))if(b.searchincludes(s=a.substr(j++,i))<0)s][0]
document.write("<pre>"+
[ [ "test", "best" ], [ "wes", "west" ], [ "red", "dress" ] ]
.map(c=>c+": "+solution(c[0])(c[1])).join`\n`)
Test works only in Firefox. Returns undefined
if there is no substring.