In a statement the RFU said the two players had been excluded from the camp in Teddington for "team culture issues".
They said they would make no further comment.
Players at the camp are preparing for the November tests against Argentina, Australia and Samoa.
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Leicester centre Tuilagi has 26 international caps but has not played for England this year due to a knee injury, although he was expected to feature in coach Eddie Jones' plans for the forthcoming matches.
He last featured in the 2016 Six Nations.
Tuilagi's ill-discipline has caused him trouble before, most notably when he was left out of England's 2015 World Cup squad after being fined for assaulting two female police officers.
Following England's exit at the 2011 World Cup in New Zealand, Tuilagi was detained by police and subsequently fined by the RFU for jumping into Auckland harbour from a ferry during a post-match party.
New Zealand-born former rugby league player Solomona has two England caps, scoring a try on his debut against Argentina.
(Reporting by Martyn Herman; Editing by Gareth Jones)
