Do both P8 AND N8 need to equal E1 for the TRUE condition of the if to be returned? If so then:
=IF(AND('Fill Info.'!P8=LogBook!$E$1,'Fill Info.'!N8=LogBook!$E$1),'Fill Info.'!H8,"")
If only one or other needs to equal E1 then:
=IF(OR('Fill Info.'!P8=LogBook!$E$1,'Fill Info.'!N8=LogBook!$E$1),'Fill Info.'!H8,"")