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Hiram, shipmen and servants of Solomon brought either 420 or 450 talents of gold. Which number is right? The context in which it is written clearly points to the one and the same event, yet with apparently different numbers.

The wages of Hiram and his servants' (workers) was 30 talents of gold. There is no contradiction. The King James Bible is always correct.

No, they aren't talking about exactly the same trip. It's the similar sentence structure of the locations that causes confusion at first glance, but careful examination of the words in between reveals the truth.

1 Kings 9
26 And king Solomon made a navy of ships in Ezion-geber, which is beside Eloth, on the shore of the Red sea, in the land of Edom.
27 And Hiram sent in the navy his servants, shipmen that had knowledge of the sea, with the servants of Solomon.
28 And they came to Ophir, and fetched from thence gold, four hundred and twenty talents, and brought it to king Solomon.

2 Chronicles 8
17 Then went Solomon to Ezion-geber, and to Eloth, at the sea side in the land of Edom.
18 And Huram sent him by the hands of his servants ships, and servants that had knowledge of the sea; and they went with the servants of Solomon to Ophir, and took thence four hundred and fifty talents of gold, and brought them to king Solomon.

There are two key differences:

First, the Kings account has Solomon make a navy of ships; in Chronicles Huram sends him [his own] ships. We know Solomon and Huram each had their own ships because of 1 Kings 10:11, 2 Chronicles 9:21, and most explicitly 1 Kings 10:22.

Second, in Kings Solomon makes the navy in Ezion-geber, which is beside Eloth; in Chronicles he goes to Ezion-geber AND to Eloth. So Solomon's ships left from Ezion-geber and Huram's left from Eloth.