Elizabeth
There is a guide to Permitted Work in the ESA section
www.benefitsandwork.co.uk/help-for-claimants/esa1 I'm afraid we do not advise on Tax Credits, but you would need to close your ESA claim to qualify. ESA does not allow you to work the 16 or more hours a week that Tax Credits require as a minimum.
If you close your ESA claim then you can make a rapid re-claim with 12 weeks, if you need to claim ESA again after the 12 weeks have elapsed then it will be treated as a new claim, if your current claim is Contribution Based then you would also be required to re-meet the Contribution Conditions.
Gordon