This information is available (in English) at www.bdz.bg. I don't know your dates of travel but at the moment it shows a direct overnight train leaving Sofia at 22.15 arriving Burgas 06.05. There are several daytime trains too. The standard 2nd class single fare is shown as about 17 leva with sleeper supplement 8 leva - but there are various options so check yourself for your exact date/time of travel.
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