The philosophers Jean-Paul Sartre and Albert Camus are better known for their enmity than friendship.

But long before the pair had a very public falling-out over the necessity of "revolutionary violence" – Sartre for, Camus against – they were on talking and socialising terms a newly discovered letter has revealed.

"My dear Sartre," Camus opens in the short hand-written missive. "I hope you and Castor are working a lot … let me know when you return and we will have a relaxed evening."

Castor was Sartre's pet name for his partner and fellow philosopher and writer Simone de Beauvoir.

The letter was found by two booksellers in Orléans in an original edition of a book, only 60 copies of which were published in 1966, of Sartre's writings.

It is not dated but is believed to have been written between 1943, when the men met, and 1948 when they were good friends. They fell out in 1952.

"The letter is very important because it shows that despite what some writers have said, Sartre and Camus, had a close friendship," Ronald Aronson, a Sartre specialist told the French newspaper Libération.

The letter, on headed paper from the philosophers' publishers Gallimard, was discovered by Hervé and Eva Valentin, organising an exhibition in Lourmarin, Vaucluse, where Camus is buried, in September to mark the centenary of his birth.

In her autobiography La force de l'age (The Prime of Life), De Beauvoir recounts how Sartre and Camus met at the production of one of Sartre's plays in 1943.

Sartre had previously written a superb critique of Camus' celebrated work L'Etranger (The Outsider).

"We have done some bad work, my friends and I; so bad that I'm sleeping badly," Camus' letter continues in reference, it is believed, to an aborted plan to stage one of his plays.

Eva Valentin said much of the short letter remained a mystery. "There's no answer, no reliable source to shed light on the mystery as all correspondence between the two men has been destroyed," she told AFP.

• This article was amended on 9 August 2013. It originally said the letter was found by two librarians – a mistranslation; they are booksellers - and "beaucoup travailler" was translated as "lots of work" rather than "working a lot".