1. Use grep -Eo: (as egrep is deprecated)
echo 'employee_id=1234' | grep -Eo '[0-9]+'
1234
2. using grep -oP (PCRE):
echo 'employee_id=1234' | grep -oP 'employee_id=\K([0-9]+)'
1234
3. Using sed:
echo 'employee_id=1234' | sed 's/^.*employee_id=\([0-9][0-9]*\).*$/\1/'
1234