I have a log file (application.log) which might contain the following string of normal & special characters on multiple lines:
*^%Q&$*&^@$&*!
Tell grep to treat your input as fixed string using -F option.
grep
-F
grep -F '*^%Q&$*&^@$&*!^@$*&^&^*&^&' application.log
Option -n is required to get the line number,
-n
grep -Fn '*^%Q&$*&^@$&*!^@$*&^&^*&^&' application.log