Not all mate-in-10s are hard to solve. Many follow concrete mechanisms involving move-repetitions. This one, for instance, is a good example. White to play and mate in 10. Find the key move.
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Black evades the mate threat with 1... Ke5. How should White proceed from here?
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2. Bxc3+ Kd6 - How should White continue?
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3. Nf7+ Kc5 - White to play. Keep going.
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4. Bb4+ Kd4 - White to play. A key move needs to be found here!
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5. Bf1 c3 - How does White continue from here?
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6. Ng5 Ke5 - How does White proceed?
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7. Bxc3+ Kd6 - Keep going. White to play.
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8. Nf7+ Kc5 - Keep going. White to play.
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9. Bb4+ Kd4 - Now that the c3 pawn is eliminated, how does White finish off the game?