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Wealth alone doesn't bring happiness.
Literal
Wealth [topic-は] that-alone [with-で] [topic-は] happiness [object-を] does-not-bring.
それだけでは stacks three elements: それ (that) + だけ (only) + では (as for/by) — meaning 'by that alone.' もたらさない is the negative of もたらす ('to bring about'). A philosophical statement about wealth's limits.