This question has come up a lot before, and the answer is basically "if you really have no idea what adapters were used, you're screwed", because we don't have any tools to identify custom adapter sequences yet. You can detect over-represented sequences, but this is really a different sort of problem. The exception is BBMap which can remove custom adapters if you have very short insert-lengths and paired-end sequencing, thus adapters are routinely sequenced into a lot, and the paired-end sequencing allows you to distinguish insert from adapter very clearly. But again your insert length has to be consistently shorter than the read length.
If you know that your adapter is a standard adapter, you just don't know exactly which one, then that's a different (and much simpler) problem than finding a custom adapter. For this you just need to point a trimming tool like Picard's MarkAdapters to your reads, and provide it with a list of all possible adapters (built in to the Picard MarkIlluminaAdapters if you're using Illumina), and it will remove all adapter sequences, and count the number of times each adapter sequence was removed, from which you can determine the adapters used. You might have to re-run the adapter marking tool now that you know the actual adapter sequence, although perhaps Picard automatically does this for you. Not sure.
There's enough tough questions to answer in Bioinformatics, and solving man-made problems like figuring out the adapter sequence used isn't a top priority for many tool designers, unfortunately. However given the funding (or lack of) it's not surprising.