You cannot deduct a gift that you made to your brother. It is still taxable to you.
You took a $10,000 distribution from your IRA. That makes it taxable income to you. Any withdrawal from an IRA is taxable income. It doesn't matter what you did with the money after you took it out of your IRA.
I'm not sure what you mean by "the 10% tax underpayment." Do you mean the 10% penalty for an early withdrawal before you are 59 1/2 years old? That penalty doesn't apply to withdrawals from an inherited IRA.
Or did you receive a penalty for underpayment of estimated taxes?
Were you trying to give your brother part of the IRA money and maintain its status as an IRA? Did you intend to share the inherited IRA with your brother? There's no way to do that. If the person from whom you inherited the IRA intended it to be shared between you and your brother, he or she should have designated both of you as beneficiaries. Now that you have inherited the entire IRA yourself, there is no way to make part of it an IRA for your brother.
If your intent was to share $10,000 of your inherited IRA balance and you not have to absorb the tax consequences of the $10,000 distribution from the IRA, your gift to him should have been reduced by the increase tax liability that you incurred by you receiving the $10,000 distribution. For example, if your marginal tax rate (federal and state combined) is, say, 30%, you would gift him $7,000 and use the other $3,000 to pay your federal and state income taxes.