There are no single English words that meet the criteria. The only 6-letter word you can make with those letters is aerugo.
betake
sexe
Hanger is a six letter word.
Warble, bawler
GIGGLE
the six letter word with e as second letter and 5th is... SECRET jestermeltedbeltedtendertendedmendeddealerheaderLentensedges
novice
blunge, bungle
Some six letter words with second letter E and ending in ER are:beakerbearerbeaverbeeperbenderbettercenterdealerdearerfeederfeelerfenderfestergendergeyserheaderhealerheaterheiferhelperherderjesterkeeperleaderleanerlecherledgerlenderlettermeanermeekermembermergernearerneaterneuterpeeperpelterpepperpesterpewterreaderreaperrenderrentersealerseekersellersenderserversettersexierteaserteetertellertempertendertestertethervergervesperweakerweaverwelderwelter
Those letters will make the word 'stolen', but you can't make an eight letter word with six letters.
engulf
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