I have no personal experience of bus travel in/from Tunisia but I checked the SNTRI site. No bus to Algeria is listed. I've noticed that shared taxi from Tunis to Annaba seems to be the norm, but I cannot be certain how recent or accurate that information is..nor, indeed, how accurate the info on the SNTRI site is.
You could try asking at the ticket offices (guichets) at Bab Aliqua, Bâb El Fellah and/or Bâb Sâadoun:
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