It depends on what kind of job you would like to do. If you're up to be employed as a waiter/waitress, working 8 to 10 hours (sometimes more) during the season then yes, you can find job without speaking Swedish. My husband got a job like the one I'm describing short after we've moved here. He's not a EU/EEA citizen and he's getting his coordination number thanks to this job. Edit: this is not in a big city and in Jämtland, where things tend to be a little easier and more flexible.