Mahatma Gandhi speaking at a conference in 1947.
I can't find a source for this quote attributed to Gandhi. The meaning may be taken from parts of Gandhi's speech at a conference in 1947 (he's giving this speech in the photo above) where he asks that people who want to communicate truth, especially when they do no agree with each other, should use both their heads and their hearts, and deliver the message with real understanding and not vengeance.
"What I want you to understand is the message of Asia. It is not to be learnt through the western spectacles or by imitating the atom bomb. If you want to give a message of truth. I do not want merely to appeal to your head. I want to capture your heart.Mahatma Gandhi Information Website, Famous Speeches Of Gandhiji, Speech Before Inter-Asian Relations Conference, April 2, 1947>>
In this age of democracy, in this age of awakening of the poorest of the poor, you can redeliver this message with the greatest emphasis. You will complete the conquest of the West, not through vengeance, because you have been exploited, but with real understanding. I am sanguine, if all of you put your hearts together – not merely heads – to understand the secret of the message these wise men of the East have left to us, and us if we really become worthy of that great message, the conquest of the West will be completed. This conquest will be loved by the West itself.
The West is today pinning for wisdom. It is despairing of a multiplication of the atom bombs, because the atom bombs mean utter destruction, not merely of the West, but of the whole world, as if the prophecy of the Bible is going to be fulfilled and there is to be a perfect deluge. It is up to you to tell the world of its wickedness and sin – that is the heritage your teachers and my teachers have taught Asia."