You would need to perform a baseline change to add the resource and work/cost to that task, and thus the total budget. at the point in time mandated by your baseline change management process. The presumption on my part is that scope is either being increased, or that the work is behind schedule, thus the need to add resources. This would need to occur even if another task was being reduced and the increase in cost for the in question was being offset by that reduction. BOTH tasks would then need to be re-baselined.
One wouldn’t normally change resource/cost/schedule in an EV environment without updating the baseline, and yes, it would most likely mess up your EV and violate good EV practice (and the law if you were working on a Defense Department project).