Novice soldering - burnt board
Yes, you should be able to solder that back. Be 100% sure to use electronic grade flux core solder and not plumbing solder. 

It looks to me like the assembler was rough and cracked the solder joint (latent failure), which then oxidized and heated up causing the damage you see. The heating is apparently confined to just the joint area, so I don't think anything else is wrong. 

Maybe try cleaning the area with an old toothbrush and isopropanol and then gently scraping the solder mask off (leaving clean copper) around the connections. If the connection doesn't look perfect, lay a wire from the pads to that bare section of the trace it connects to and run solder all over it.