Barney uses 2 clean towels every day, so he uses 2 * 7 = <<2*7=14>>14 towels a week.
He missed one week of laundry, so he would need 2 * 14 = <<2*14=28>>28 towels for 2 weeks.
He owns 18 towels, so he has 28 - 18 = <<28-18=10>>10 less than he needs.
Thus, Barney will not have clean towels on 10 / 2 = <<10/2=5>>5 days.
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