You can decline without a TED talk. “I can’t make it” is a finished thought.

A refusal does not need a case attached to it. Building an argument implies the other person is entitled to weigh your reasons and rule on them, which turns a simple no into a negotiation you never meant to open. The long explanation usually comes from discomfort rather than courtesy.

Try the short version next time: you cannot make it, and you hope it goes well. Resist filling the pause that follows. Most people accept it immediately, and anyone who pushes is telling you something useful about the relationship.