'come up with' suggest or create find a solution It could also mean present, originate or invent. 'come up with an idea' 'come up with creative themes.' 'He came up with an elegant solution to the problem.' 'bring up' means initiate,mention in conversation. It could aslo mean introduce, discuss or raise. "I hate to bring this up, but we I am afraid we have to discuss this matter as soon as possible." ** Notice that 'bring up' could have another meaning ,to rear or educate a child.**

When you use "come up with" it means getting an idea or plan. For example: MAN: We need to solve this problem about the economy. What have you come up with? WOMAN: I have some ideas to solve the problem. "Bring up" means to say something that happened in the past. For example: MAN: Why do you have to bring up what happened two years ago? I don't want to talk about it anymore. WOMAN: But if you don't talk about what happened then you'll never be healed.

You come up with a new idea. You bring up an old topic.