Let dopen = decimal odds on open bet
Let dnew = decimal odds on new bet
Let M = money wagered on open bet
Let X = necessary money to wager on new bet in order to equalize losses
M*(dopen-1) - X = X*(dnew-1) - M
X = M * dopen / dnew
So in the examples you gave:
M = $5,800
dopen ≈
new ML = -110
dnew ≈
X ≈ $5,800 * 1.86207 / 1.90909 ≈ $5,657.15
new ML = +105
dnew =
X ≈ $5,800 * 1.86207 / 2.05 ≈ $5,268.30
That said, equalizing losses should not generally be the goal of the advantage middle player. Ostensibly, your first bet was +EV, while the second was at-market.
As such, you'd likely want to risk less on the second wager than indicated above, leaving yourself some additional exposure to the first wager. The decision of exactly how much to wager on the second could best be answered by appealing to a staking strategy such as Kelly.