Does anyone know an algorithm to swap two edges in this position, without scrambling the first two layers?

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Disclaimer: Possible duplicate of (Swap the edges in a solved Rubik's cube). I would post this as a comment, but I don't have enough rep to do so yet :P

Short answer: it's not possible to solve, and you can't get to that configuration from a standard Rubik's Cube in the first place.

You will find the answer and explanation to your exact question in the above link.

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    $\begingroup$ Welcome to PSE (take the tour)! Suggestion: turn this into an actual answer by bringing in the relevant information from that link (still link to it as an original source). Then this post won't get deleted as "not an answer", and you'll earn the rep you need to post actual comments in the future. :) $\endgroup$ – Alconja May 30 '18 at 2:11
  • $\begingroup$ @Alconja the link is to a puzzling.stackexchange site. I think this question should be closed as a duplicate. $\endgroup$ – BittersweetNostalgia May 30 '18 at 2:35
  • $\begingroup$ Ahh apologies, didn't notice the link was internal. I'll vote to close as a duplicate. Thanks for spotting. In future, I believe you can flag a post as a duplicate, even as a low rep user, and whilst that won't count as an official vote to close, it will bring it to the attention of reviewers. $\endgroup$ – Alconja May 30 '18 at 2:44

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