there is gap of 2years after 10th and before polytechnic . however, can i take ssc je exam ?
There is not a matter whether you have taken any gap or not, you will be always eligible for any type of exams and admission.
As you are thinking to give the SSC JE exam so there also they don't care if you have taken a gap year or not. They might ask you during the interview these type of question but still that is not a big deal, you can simply explain your problem.
Good luck :)