Lookup and Display of Matched Cell Data?

Supposed your dates are in A1:A365, amount in B1:B365, your seach amount in E2, return date in F2.
In F2:

=MATCH($E$2,$B$1:$B$365,-1)+IF($E$2>=AVERAGE(INDEX($B$1:$B$365,MATCH($E$2,$B$1:$B$365,-1)),INDEX($B$1:$B$365,MATCH($E$2,$B$1:$B$365,-1)+1)),0,1)